Tips to achieve better oscilloscope measurements

Most engineers always have so much to do but not enough time to do them. Thus, they wanted an oscilloscope that will help them reduce the time spent on researching how to make a measurement, and spend more of it in troubleshooting.

Although some high-performance oscilloscopes make it easier for engineers to accomplish simple tasks, providing them with easy access to advanced functionality, this article also offers some tips on how they can increase their effectiveness in making critical measurements.

First, never forget to check the probe. Engineers usually forget to check probe compensation prior to making amplitude measurements on the sinewaves, particularly when their not working with a fast risetime. However, they tend to ignore the fact that risetimes within the measurement system of the oscilloscope also have its effect, which can cause errors when measuring signals.

Second is to find a quick way to troubleshoot mixed hardware/software prototypes. Troubleshooting and designing hardware driven with software commonly requires engineers to look at complex and lengthy bit streams. This is solved by finding an unused I/O pin, which they can use as a trigger point, and inserting the code into the software to easily toggle the pin at the right time. This process help engineers save the trouble of learning complex oscilloscope features, while providing them full control through SW of where the trigger will occur.

The third tip is to use two oscilloscope channels when measuring low frequency signals. To quickly eliminate the noise, users should set one input to ac coupling and the other to dc coupling, while ensuring that both carry similar amplitude range. The oscilloscope should then be set to display CH1 – CH2 (or invert one of the channels and add them), with both probes applied on the test point. This will subtract out the ac component, leaving only the ac component that is lower than the oscilloscope’s ac coupling frequency and the dc component.

The fourth tip is to be intimate with the noise. When chasing unknown intermittent noise source, it helps to know more about it. One useful characteristic is to determine the initial noise transition’s direction. If it is negative-going, the change could be caused by a voltage drop. If it is positive, it could be caused by some kind of inductive surge.

The next tip is to create a “bargain basement” magnetic probe. This is done by connecting the ground lead of the oscilloscope probe to its tip. Engineers can then sniff out oscillations including other sources of the noise on the DUT without even touching it. This will also help engineers check cabinets for EMC leaks and determine optimal cable routing. It should be noted that when snooping, magnetic signals are at their strongest whenever the loop is at 90° to the signal.

Finally, it is worth noting that custom graticules work for almost any oscilloscope. Although oscilloscopes nowadays offer specialized measurements on complex waveforms such as eye diagrams, it is sometimes simpler and faster to work with the device on hand. Consider using easily available and cheap materials such as Chartpak tape as well as transparency materials to make templates that can be taped on the oscilloscope screen. This allows users to work from templates found in specification documents or make templates from “golden waveforms” that were captured on screen.

Tips to save time when using an economy oscilloscope

When operating on a tight budget and in need of a new oscilloscope, users would often settle for an oscilloscope that features bare bones capability. However, with the economy oscilloscopes offered in the market nowadays, users need not suffer for their limited budget. They simply have to consider these five simple tips.

For optimum results, users should first consider the bandwidth, memory depth and sample rate of the oscilloscope.

The oscilloscope’s main function is to deliver an accurate representation of the signal viewed, and the combination of bandwidth, memory depth and sample rate determines the oscilloscope’s ability to accurately display the signal. To ensure that the oscilloscope has adequate bandwidth, users should consider the fastest signal rise time that needs to be viewed and use the formula:

Scope bandwidth = 2 X signal bandwidth, where signal bandwidth =1/ (2 X signal rise time).

To avoid missing key signal transitions, the sampling rate of the oscilloscope should be at least four times than its bandwidth.

Users should also select an economy oscilloscope with deeper memory. This enables the oscilloscope to store more data points over the acquisition period, allowing users to view the entire signal and still zoom in on specific areas of interest.

The second tip is to use the oscilloscope’s built-in measurement capability to eliminate errors and save time.

When recording critical information about the signal, such as peak-to-peak voltage or frequency, most of today’s economy oscilloscopes eliminate the need for manual effort and tendency for errors in calculations or readings. These oscilloscopes can calculate and display various voltage and time measurements with a simple touch of a button.

The third tip is — when in doubt as to how to trigger on the problem, users should utilize sequence mode to isolate specific areas of interest. Once the unexpected anomalies have been identified, users can refine the trigger conditions to determine the root cause.

When making the next oscilloscope decision, users should consider whether the sequence mode would provide benefits in their common tasks.

The next tip is to use pass/fail (go/no-go) mask testing to isolate problems or to make quick decisions.

Mask testing can be a very helpful tool as it allows users to know whether certain signals have to be within specific ranges for the design to properly work. Several economy oscilloscopes offer this kind of capability, enabling users to capture a “golden” waveform as well as define tolerance limits for correct performance.

The last tip is to consider usability. Users should choose an oscilloscope that features menus that are easy to navigate, showing the choices in dropdown selections. One of the clearest time savers is simultaneously displaying on the screen the entire captured waveform and the specific area of interest that the user have zoomed in. This allows users to view the big picture as well as the details of the signal all at once.

How to select the right handheld oscilloscope

Aside from characterizing microelectronics to troubleshooting process controls, multi-industrial automation, automotive-service industries and facility maintenance, handheld oscilloscopes can also offer the performance of bench oscilloscopes in a mobile and rugged form factor.

Generally, handheld oscilloscopes integrate test tools specifically designed for field use where the conditions are dangerous, rigorous and precarious. It has to be noted, however, that handheld oscilloscopes are not designed equal. Hence, it is advantageous for users to compare some of its important specifications, such as bandwidth, sample rate and memory depth, before deciding on which one to purchase.

Users should also take into consideration the number of channels, channel isolation capability and safety ratings of the handheld oscilloscope.

Most oscilloscope users erroneously believe that bandwidth determines the highest frequency that can be captured. However, oscilloscope’s bandwidth refers to the frequency that the input signal is attenuated by three dB, which translates to around -30 percent amplitude error. This implies that signals cannot be accurately captured near the oscilloscope’s bandwidth.

When choosing a handheld oscilloscope, users should pick one with a bandwidth that is five times more than the highest frequency that has to be captured.

Another mistaken assumption is that an oscilloscope with a higher sample rate is better than one with a lower sample rate. In truth, an oscilloscope offering higher sample rate does not necessarily offer any extra benefit when compared to an oscilloscope with a lower sample rate.

For a faithful reproduction of a signal on an oscilloscope, Nyquist’s sampling theorem provides that the oscilloscope’s sample rate should be more than double the signal’s highest frequency. This means that if a 40 MHz signal is to be captured, the sample rate of the oscilloscope should be at least 80 MSa/s.

Captured data are stored in the oscilloscope’s waveform buffer and the size of its buffer memory is known as the memory depth. An oscilloscope with deep memory allows users to keep a higher sample rate for a longer period of time.

The memory buffer is quickly filled at high sample rates. Thus, an oscilloscope with a limited memory depth and a high sampling rate of up to two GSa/s can collect data only if it reduces its sample rate. This will prevent the oscilloscope from capturing waveform accurately since the sample points are placed too far apart from each other. However, an oscilloscope that offers deeper memory can sustain its maximum sampling rate, allowing it to accurately capture the waveform.

Oscilloscopes are available in two-channel and four-channel varieties. Each channel allows users to record and measure one signal at a time. In deciding which oscilloscope to purchase, a user should determine the number of signals the user wanted to display on the oscilloscope.

Oscilloscopes with four independently isolated channels are generally used when simultaneously viewing three or more signals, such as when troubleshooting three-phase applications like industrial motors, high-power inverters and variable-frequency motor drives. These kinds of oscilloscopes are rarely used and are usually more expensive. Most of the time, users will only need two channels.

Digitizing Oscilloscopes

One of the important signal integrity measurement solutions is the digitizing oscilloscope.

Digitizing oscilloscopes have different forms — the sampling oscilloscope, the digital phosphor oscilloscope (DPO) and the digital storage oscilloscope (DSO).

Ideally suited for low-repetition signals with narrow pulse widths or fast edges, the DSO can easily capture transients and one-time events, and is the best solution for multi-channel, high-speed design applications.

The DPO, on the other hand, is the perfect tool for digital troubleshooting, for identifying intermittent signals and for various kinds of mask testing and eye diagram. The extraordinary waveform capture rate of the DPO overlays sweep after sweep of data more easily and quickly than other oscilloscope, offering frequency-of-occurrence details, in intensity and colour, with unrivalled clarity.

The digital sampling oscilloscope is the tool of choice when the real-time oscilloscope’s bandwidth is not enough. It is ideal for capturing repetitive signals with much higher frequency components than the sample rate of the oscilloscope. Measuring signals faster than other oscilloscopes, the digital sampling oscilloscope can also achieve up to 100 GHz bandwidth using sequential equivalent-time sampling of repetitive signals.

In selecting an oscilloscope, users should take note of several performance considerations that affect the quality of signal integrity measurements. These include rise time, bandwidth, record length, waveform capture rate, triggering flexibility and sample rate.

Rise time measurements are important in the digital world. Rise time is the more appropriate consideration when selecting an oscilloscope to measure digital signals such as steps and pulses.

Generally, an oscilloscope with rapid rise time can more accurately capture the fast transition’s critical details. The rise time taken by oscilloscope depends on both the rise time of the oscilloscope and the actual rise time. Faster oscilloscope rise time results to more accurate rise time measurements.

Meanwhile, oscilloscope bandwidth is critical when troubleshooting designs with fast rise time signals or high data rates. The digital signal’s rise time carries higher frequency components than what is implied by its repetition rate. To capture the higher frequency components, the oscilloscope should have adequate bandwidth while showing signal transitions accurately.

The oscilloscope cannot resolve high-frequency changes without sufficient bandwidth, while its special features and strengths will mean nothing.

Record length refers to the number of samples that an oscilloscope can store and digitise in one acquisition. With the oscilloscope storing only a limited number of samples, the length of time captured or the waveform duration will be inversely proportional to the sample rate of the oscilloscope.

Expressed as waveforms per second (wfms/s), the oscilloscope’s waveform capture rate determines how often the oscilloscope captures a signal, while the oscilloscope’s sample rate shows how frequently it samples the input signal in a cycle or waveform.

Oscilloscopes nowadays provide triggers for various analog events, including slew rate conditions and edge levels; low-amplitude events and events width conditions; pulse characteristics; serial data patterns as well as setup and hold time violations.

These trigger types assist engineers in isolating and detecting signal integrity problems. The digitizing oscilloscope also features various combinations of timing, logic triggers and voltage as well as specialty triggers, for applications like serial data compliance testing.

Oscilloscope: A Power Measurement Tool

Power supply refers to a subsystem, component or system that transforms electrical power from a particular form to another, usually converting alternating current (AC) to direct current (DC) power. It has to be noted that the proper operation of electronic equipment, which range from personal computers to industrial machinery and military equipment, relies on the reliability and performance of DC power supplies.

Oscilloscope’s power supplies come in various kinds and sizes, from conventional analog types to highly-efficient switch-mode power supplies, with each of them facing a complex, dynamic operating environment. Device demands and loads can significantly change from one instant to the other. A commodity switch-mode power supply has to survive sudden peaks, exceeding its average operating levels.

Characterizing a power supply’s behavior means taking voltage measurements and static current with a digital multimeter and painstakingly making calculations on a PC or a calculator. However, most engineers nowadays consider oscilloscope as one of the preferred power measurement platform. Equipped with integrated analysis and power measurement software, the oscilloscope simplifies set up, making it easier for users to take measurements over time. The oscilloscope even allows users to automate calculations, customize critical parameters and view results.

Ideally the behavior of every power supply is similar to the mathematical model employed to design it. However, in reality, loads vary; components are not perfect; changes in the environment affect performance and line power could be distorted.

Thus, designers are required to create a power supply that occupies less space, meets tougher EMC/EMI standards, cuts manufacturing costs and reduces heat. Engineers can achieve these goals by using a rigorous regime of measurements.

With their relatively low frequencies, power measurements may appear simple to users used to taking high-bandwidth measurements using an oscilloscope. On the contrary, power measurement present users with a plethora of challenges that has never been confronted by a high-speed circuit designer. The voltage on a switching device can be rather huge, and could be “floating”, which means that it is not referenced to the ground. Variations could be observed in the signal’s period, pulse width, duty cycle and frequency. Waveforms should be faithfully captured as well as analyzed for imperfections.

The demands presented on the oscilloscope are exacting, with various probe types single-ended, current and differential required simultaneously. The device should have a deep memory in order that it can deliver the record length required by long, low-frequency acquisitions. It may even be required to capture signals of widely different scales in a single acquisition.

When preparing the oscilloscope for power measurements, users should ensure that it offers the basic sample rate and bandwidth required to handle the switching frequencies across a Switch-mode power supply (SMPS). Power measurements demands at least two channels, one for current and one for voltage. Users should also note that the facilities used to take power measurements are easy to operate and are reliable. Users should also have accurate voltage and dependable current probes, in order that they can align differing delays expediently.

Understanding Oscilloscopes

The oscilloscope is one of the most indispensable equipment in an engineer’s lab. Thus, it is important for users to have a working knowledge of its functions, principles and parts.

A digital storage oscilloscope works by sending a signal to the vertical amplifier through the probe. The signal is then digitized by the analog-to-digital converter (ADC) by sampling it at separate points in time. At these points, the signal’s voltage is converted into digital values known as sample points.

The sample points are stored in the acquisition memory as waveform points, which comprise one waveform record.

Record length refers to the number of waveform points used to form a waveform, while trigger determines the record’s start and stop points.

The oscilloscope’s signal path includes a microprocessor that measures and formats the signal for display. The signal then travels via the display memory before they are displayed on the screen.

One of the important principles that users should learn about oscilloscope is that it is generally a device that creates a graph of an electrical signal.

The graph indicates how signals change over a certain period of time — the horizontal (X) axis represents the time, while the vertical (Y) axis represents the voltage. The waveform’s brightness or intensity is often called the Z axis.

In addition, the key specifications of the oscilloscope include bandwidth, which refers to the frequency range of the device; record length, refers to the number of waveform points utilized to create a record of a signal; and sample rate is the frequency that the oscilloscope samples a signal, which is specified in samples per second (S/s).

The front panel of an oscilloscope has three main sections.

The first is the vertical system and controls that consists of the position and volts-per-division (volts/div), input coupling, DC coupling and AC coupling.

The oscilloscope’s vertical position control enables users to move the waveform up and down the display, while the volts-per-division (volts/div) setting allows the user to change the waveform’s size on the screen.

DC coupling shows the entire input signal, while input coupling indicates which part of the signal for input is viewed on the screen.

AC coupling blocks the signal’s DC component in order that the waveform may be centred on zero volts. The input signal is disconnected from the vertical system by the ground coupling to allow users to view the location of the zero volts on the screen.

The oscilloscope’s horizontal position allows users to move the waveform left to right on the screen, while its seconds-per-division (sec/div) settings changes the rate that the waveform is drawn on the screen.

Meanwhile, the trigger functions of the oscilloscope synchronize the horizontal sweep at the signal’s correct point. The trigger controls enable users to capture single-shot waveforms and stabilize repetitive waveforms. To make repetitive waveforms appear static, the oscilloscope’s trigger repeatedly draws the trace at similar parts of the waveform.

The trigger circuit serves as a comparator, where users can select the voltage and slope level on one of the input comparator. The oscilloscope produces a trigger whenever the trigger signal on the other comparator input matches the setting selected by the user.

Selecting the best active and passive oscilloscope probes

To achieve reliable oscilloscope measurements, users should first determine the proper probe for their application. There are two main categories of oscilloscope probes — passive and active probes.

Passive probes do not need external probe power, and can be grouped into two major types — low-impedance resistor-divider probes and high-impedance-input probes.

Shipped with most mid- and low-range oscilloscopes, the high-impedance-input passive probe that features a 10:1 division ratio is today’s most commonly utilized probe.

Unlike active probes, passive probes are less expensive and more rugged. They provide wide dynamic range as well as high input resistance to match the input impedance of the oscilloscope. However, high-impedance-input probes require heavier capacitive loading and offer lower bandwidths than low-impedance (z0) resistor-divider passive probes or active probes.

Meanwhile, the key benefits offered by low-impedance resistor-divider probe include very low capacitive loading and remarkably high bandwidth, which helps achieve high-accuracy timing measurements. The probe also costs less than an active probe with a comparable bandwidth range. It can also be utilized in various applications, such as probing 50 Ω transmission lines, electronic circuit logic (ECL) circuits and microwave devices. However, one crucial trade-off of this probe is its relatively heavy resistive loading that can affect the signal’s measured amplitude.

Active probes are employed when utilizing an oscilloscope with over 500 MHz of bandwidth. It is the tool of choice when users need high-bandwidth performance. Costing more than passive probes, active probes offer limited input voltage. Their significantly lower capacitive loading enables them to deliver more accurate insight into fast signals.

Active probes require external probe power for its active components, such as amplifiers and transistors. Most contemporary active probes depend on intelligent probe interface that not only provide power, but also serve as communication links between the oscilloscope and the compatible probes. The probe interface usually identifies the kind of probe attached and sets up the proper attenuation ratio, input impedance, offset range and probe power needed.

To measure single-ended signals, users would usually select a single-ended active probe, while picking a differential active probe for determining differential signals. The ground plane of differential probes can effectively connect the device-under-test (DUT) to the probe tip ground than the ground connections of single-ended probes. This implies that differential probes are more ideal than single-ended probes when measuring single-ended signals.

Another clear advantage of active probes over passive probes is higher bandwidth. However, probe users often ignore the effect of the connection to the target, known as the “connection bandwidth”. Thus, even if an active probe offers remarkable bandwidth specification, the published specified performance is provided as ideal for probing conditions.

In addition, most people believe that probe impedance is constant. It is not. In fact, input impedance decreases over frequency.

At low frequency ranges and DC, the input impedance of the probe begins at the rated input resistance, and as the frequency rises, the probe’s input capacitance starts to shorten, while its impedance begins to drop.

Understanding Oscilloscope Probes

An oscilloscope is just a piece of a system that indicates how accurately users analyze and display signals. To connect the device under test (DUT) into the oscilloscopes, users will have to use probes, which are critical in terms of signal integrity. Thus, a users with a 1 GHz oscilloscope and using a probe that supports 500 MHz bandwidth, is not fully utilizing the oscilloscope’s bandwidth.

No probes can perfectly reproduce signals since the moment probes are connected to a circuit, it becomes part of the circuit, allowing portions of the circuit’s electrical energy to flow through the oscilloscope probe. This event is known as loading. There are three kinds of loading — capacitive, resistive and inductive.

Capacitive loading can slow down rise time as well as reduce bandwidth. To effectively reduce capacitive loading, users should choose a probe that has at least five times the bandwidth of the signal.

Resistive loading, on the other hand, causes the amplitude of the displayed signal to be incorrect. It can also make a malfunctioning circuit to start working whenever the probe is connected. Users should ensure that the resistance of the probe is ten times more than the resistance of the source, so that it can achieve an amplitude reduction of below ten percent.

Inductive loading appears as ringing in the signal, primarily attributed to the probe ground lead’s inductive effects. Hence, users are advised to utilize the shortest possible lead.

Meanwhile, probes come in various forms, such as active probes, passive probes and current probes.

In operating an active probe, users should note that the probe will need a power supply to powerup the active devices within the probe. The power supply is often supported by an external box or with a USB cable connection. It can also be supplied by the oscilloscope’s mainframe itself. Active probes utilize active components to condition or amplify a signal. These probes also have the ability to support much higher signal bandwidths, making them the probe of choice by most engineers in higher performance applications.

Aside from being more costly than passive probes, active probes are also less rugged and offer a much heavier probe tip. Despite all these, active probes deliver the best overall combination of capacitive and resistive loading while allowing users to test much higher-frequency signals.

Furthermore, passive probes feature passive components and eliminate the need for power supply during operation. This type of probe is useful for probing signals with less than 60 MHz bandwidth. When this frequency is surpassed, a different type of probe is needed, that is an active probe.

Passive probes are not only accurate and versatile — they are also rugged, inexpensive and easy to use. They commonly produce high capacitive loading as well as low resistive loading.

Different types of passive probes include compensated, high-resistance passive divider probes, low-impedance resistor-divider probes and high-voltage probes.

Usually utilized to measure the current flowing through a circuit, current probes are commonly large and feature limited bandwidth (100 MHz).

Importance of a deep memory in oscilloscopes

Regardless of the application, an oscilloscope with deep memory offers numerous advantages that are difficult to live without. Thus, it is vital for users to understand the importance of a deep memory.

The sample rate of an oscilloscope only indicates the maximum sample rate that can be achieved. To determine the sample rate, users should know the memory depth of the oscilloscope. Given the oscilloscope’s memory depth and its typical time base settings, users can then calculate its sample rate.

Oscilloscopes stores samples into memory. The bigger the memory, the more samples can be stored, and the more samples are stored, the higher the sample rate. This implies that deeper memory allows users to sustain the oscilloscope’s maximum sample rate across a vast array of timebase settings. With the higher sustained sample rate, deeper memory also offers more reliable and accurate measurements.

One of the common challenge for oscilloscope users is how to effectively capture adequate cycles of both fast and slow signals simultaneously and maintain enough resolution to zoom in and view signal details. Insufficient resolution between points, leave users in the dark of what is really going on with their design while running the risk of completely missing events like glitches or anomalies. Without a fast deep memory oscilloscope, serious problems such as these can take hours or even days to finally discover.

Also, a shallower-memory oscilloscope compromises sample rate, providing an incomplete view of the digital and analog interaction in the design.

When signals behave badly during power up, even the most powerful triggering capability of the oscilloscope won’t solve the mystery of where to start looking for the cause. The only solution to the problem would be a deep memory, which provides users the ability to observe a full-start-up cycle with high resolution at longer periods of time. This effectively enables users to trace the path between the symptom as well as the root cause.

Deep memory also plays a critical role in analyzing the spectrum of signals. The frequency resolution is related directly to the amount of time displayed on the screen, with more time offering finer resolution. In addition, the maximum frequency that users can view is tied directly to sample rate — higher sample rate enables users to observe at a higher maximum frequency. Deep memory is required in capturing and viewing at longer periods of time and at higher resolution.

Overall, deep memory offers various things that users are looking for in an oscilloscope, such as the confidence that nothing is missed. An oscilloscope with deep memory delivers high resolution waveform capture attributed to its high sustained sample rate, the ability to trace symptoms back to its main cause when a good trigger event cannot be defined, and the ability to view at longer periods of time, which is especially useful when simultaneously viewing both digital and analog signals.

Categories of oscilloscope measurements

Digital oscilloscopes enable users to perform various types of measurements on the waveform. The range and complexity of measurements offered depend on the feature set of the oscilloscope.

Oscilloscope measurements can be divided into three different categories – the vertical-axis, horizontal axis and the frequency domain.

Analyzing the vertical component of the applied signal, vertical-axis measurements depict a signal in terms of a voltage level. They can also correspond to power, current or any other physical phenomena converted to voltage through a transducer or probe.

Some common vertical-axis measurements include peak-to-peak, amplitude and RMS voltage.

Peak-to-peak and amplitude are two vertical measurements that users are often confused with. This is because they are similar for all kinds of signals, except for pulse signal.

Peak-to-peak determines the voltage difference between the high voltage and the low voltage of a cycle on a waveform, while amplitude calculates the difference between where the pulse settles at the high voltage and low voltage of the signal.

RMS calculates the waveform’s RMS voltage, a quantity that can be utilized to compute the power.

The oscilloscope’s horizontal-axis measurements enable users to analyze the applied signal’s horizontal time axis, and include measurements such as Rise Time, Pulse Width, Period and Frequency. Although the value returned is usually expressed in time, it can also be expressed as a radian, ratio or in Hertz.

Rise time calculates the amount of time needed by a signal to travel from a low voltage to a high voltage, and is determined by computing the period of time needed to go from 10 percent to 90 percent of the peak-to-peak voltage.

A positive pulse width measurement determines the width of a pulse by calculating the time needed by the wave to go from 50 percent of the peak-to-peak to the maximum voltage and back again to the 50 percent mark. Meanwhile, a negative pulse width measurement determines the width of a pulse by measuring the time spent by the wave to go from 50 percent of the peak-to-peak to the minimum voltage and back again to the 50 percent mark.

Utilizing the entire waveform in the capture window, the period determines the average time for a cycle to complete, while the frequency function measures the frequency of the waveform.

The oscilloscope’s frequency domain measurements translate a time-domain waveform using a Fast Fourier Transform (FFT), and then measuring the frequency domain’s distortion and noise characteristics. Frequency domain measurements offer phase and magnitude characteristics versus frequency.

Aside from measurements, various mathematical operations can also be performed on the waveforms, including absolute value, subtraction or addition integration and fourier transform.

Absolute value indicates the absolute value of the waveform in terms of voltage, while subtraction or addition allows users to subtract or add multiple waveforms and show the resulting signal on the screen. Integration computes the integral of the waveform, while fourier transform allows users to view the frequencies that comprise the signal.

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