# Understand Signal Analysis In The Time, Frequency, And Modulation Domains

Feb. 17, 2012
This tutorial explains the fundamentals of time-, frequency-, and modulation-domain analysis from the perspective of several examples.

Modern oscilloscopes capture, view, measure, and analyze complex RF signals in the time, frequency, and modulation domains. Time-domain analysis, the original oscilloscope function, allows users to see the signal’s modulation envelope. It also enables measurement of signal-transition times, overshoot, and other time-related characteristics.

The frequency-domain view shows the signal’s spectral content, the power distribution as a function of frequency. The modulation-domain view allows us to demodulate the signal and view the modulation data. This multi-domain analysis capability reduces the number of test instruments required to completely characterize signals and provides a simultaneous view of all domains.

We will look at a couple of examples of signals that benefit from this multi-domain analysis and show a comprehensive view of the three domains.

Example: RKE System
Let’s start with a relatively simple signal from a remote keyless-entry (RKE) system. The input signal from the RKE system is an amplitude-modulated, 315-MHz carrier as shown in the channel 1 trace (upper left-hand trace, Fig. 1).

1. In this multi-domain view of a remote keyless entry (RKE) system, Trace C1 in the upper left is the input signal being analyzed, an amplitude-modulated 315-MHz carrier.

The first step in the analysis is to demodulate the signal. Scopes accomplish this using a math operation called, appropriately, “demodulate.” It can demodulate amplitude-, frequency-, or phase-modulated signals using a complex filtering process.

Trace F1, below the input signal, shows the demodulated signal, a pulse train that’s also frequency modulated. In the bottom left-hand trace, we show a zoomed-in view of one pulse of the modulated input. Overlaid onto that is the demodulated envelope so you can see how well the demodulate function performs.

Multiple Analyses
With the signal demodulated, we can make some measurements on the pulse train. Below the display area is a series of six measurement parameters. The four on the left read the frequency, rise time, fall time, and positive overshoot of the demodulated pulse train.

The red trace F2 (below the demodulated pulse train) is a track of frequency. This is a plot of the cycle-by-cycle change in frequency plotted versus time. The track is time-synchronous with its source waveform. It is another way of demodulating a signal. It can be applied to frequency or time-interval error (TIE) parameters to provide frequency or phase demodulation, respectively. In this example, it shows that the frequency of the demodulated pulse train is hopping between two frequencies about 600 Hz apart.

The F4 trace in the upper-right corner (Fig. 1, again) is the fast-Fourier transform (FFT) of the input signal. This is the frequency spectrum of the input. The two right-hand measurement parameters of the six at the bottom display the frequency of the highest peak in the spectrum, 315 MHz, and the maximum spectrum amplitude, –38 dBm. Note that this is a 50-Mpoint FFT with a resolution bandwidth of 50 Hz.

The next lower right-hand trace, Z2, is a zoomed-in view of the spectrum peak. Below that (F5) is the boxcar-averaged view of the spectrum peak. This smoothes the spectrum and allows us to see the close-in modulation peaks due to the amplitude and frequency modulation components.

As you can see, the modern oscilloscope performs a wide range of analyses without the need for another instrument. Time- and modulation-domain views show the instantaneous changes in the signal, while the frequency-domain view shows changes averaged over the acquisition time.

Multiple FFT Analysis
However, it is possible to use multiple FFTs, of zoomed-in traces, to look at smaller sections of any acquired waveform (Fig. 2). The track of frequency in trace F2 shows regions where the pulse-repetition frequency (PRF) of the demodulated signal is changing.

2. Here we are using multiple FFTs to see the spectrum of different parts of the acquired waveform.

We have opened zoomed-in traces of an area with constant PRF (trace Z1 at lower left) and another where the PRF is changing with the encoded data (trace Z3, above trace Z1). We also show FFTs of the zoomed-in portions of the original acquisition for the constant PRF (trace F5 at bottom right) and for the changing PRF (trace F3, above F5).

Note that there are subtle differences in the spectra. The FFT trace F3 has a large number of spectral peaks superimposed over the common shape. Thus, we see in Figure 2 three FFTs showing us the frequency spectrum of the whole acquisition (traces F4 and F6) and simultaneously that of two smaller sections (F3 and F5).

Let us look at another example. In this case, we will look at a radar signal incorporating an FM “chirp.” This signal is both amplitude- and frequency-modulated (Fig. 3). The pulse shape is due to the amplitude-modulation component.

3. This screen capture depicts the time- and frequency-domain analysis of a radar signal incorporating an FM chirp.

Inside the pulse, the frequency of the carrier is being linearly swept. The upper trace shows the acquired radar pulse. Immediately below we show the demodulation of the amplitude-modulated component. This is the pulse envelope of the signal. Although not shown here, it is possible to make parametric measurements on the pulse shape as we did in the previous example.

The frequency-modulated “chirp” is extracted by another instance of the demodulate math function in the trace F2 (shown as the third trace from the top of the screen). As you see, the frequency changes linearly during the pulse.

Note that in areas outside the RF pulse, the phase shows a random variation, which is normal. The frequency variation is confirmed in the FFT shown in the bottom trace, F3. The flat-topped section shows the frequency change of the “chirp” that takes place over the entire acquisition.

Let’s look at our final example (Fig. 4). In the top trace, we have a radar pulse, which is phase-modulated using Barker codes. The second trace, function F1, uses the demodulate math function to compute the amplitude envelope of the RF pulse. This shows amplitude spikes where the Barker codes cause a change in phase. The third trace from the top, Function F2, is phase-demodulating the same RF pulse and shows the phase changes due to the coding.

4. Shown is a multi-domain analysis of a radar signal employing a phase-modulated Barker code.

Note that in areas outside the RF pulse, the phase shows a random variation. Again, this is normal. As before, the bottom trace is the spectrum of the RF pulse showing the effects of the simultaneous pulse and phase modulation.

Summary
These examples show how signals with multiple modulation types can be analyzed using three different views of time, frequency, and modulation. These views may be studied using single or multiple instances of each type.

We may examine any interesting piece of the time-domain signal in the frequency domain, with each of the views measurable with parameters. All of this analysis is available on a single instrument that improves productivity and at the same time provides a comprehensive picture of the system or device under observation.

References

LeCroy Application Briefs:

1. LAB_WM405B, “Modulation Analysis – FM” http://cdn.lecroy.com/files/appnotes/lab_wm405b.pdf
2. LAB_WM407A, “Modulation Analysis – PM” http://cdn.lecroy.com/files/appnotes/lab_wm407a.pdf
3. LAB_WM769, “Trends, Tracks, and Histograms” http://cdn.lecroy.com/files/appnotes/lab_wm769.pdf
4. LAB_WM781, “Basic Radar Measurements” http://cdn.lecroy.com/files/appnotes/lab_wm781.pdf
5. LAB_WM784, “Measurement Parameters with Pictures” http://cdn.lecroy.com/files/appnotes/lab_wm-784.pdf