Chapter 17 Signal Generation

take a relatively long time to settle. For a multitone signal, you must wait only once for the settling time. A multitone signal containing one period of the lowest frequency, actually one period of the highest frequency resolution, is enough. Once the response to the multitone signal is acquired, the processing can be very fast. A single FFT may be used to measure many frequency points (amplitude and phase) simultaneously.

There are situations for which a swept sine approach is more appropriate than the multitone. Each measured tone within a multitone signal is more sensitive to noise because the energy of each tone is lower than that in a single pure tone. Consider, for example, a single sine tone of amplitude 10 V peak and frequency 100 Hz. A multitone signal containing 10 tones, including the 100 Hz tone, may have a maximum amplitude of 10 V, but the 100 Hz tone component will have an amplitude somewhat less than this. This lower amplitude is due to the way that all the sine tones (with different phases) sum. Assuming the same level of noise, the signal-to-noise ratio (SNR) of the 100 Hz component is therefore better for the case of the individual tone. It is possible to mitigate this reduced SNR by adjusting the amplitudes of the tones, applying higher energy where needed and lower at less critical frequencies.

When viewing the response of a system to a multitone stimulus, any energy between FFT bins is due to noise or unit-under-test (UUT) induced distortion. The frequency resolution of the FFT is limited by your measurement time. If you only want to measure your system at 1.000 kHz and 1.001 kHz, two independent sine tones is the way to go. The measurement can be done in a few milliseconds while a multitone measurement requires at least 1 second. This is because you must wait for enough time so as to obtain the required number of samples to achieve a frequency resolution of 1 Hz. Some applications, like finding the resonant frequency of a crystal, combine a multitone measurement for coarse measurement and a narrow-range sweep for fine measurement.

Noise Generation

Noise signals may be used to perform frequency response measurements, or to simulate certain processes. Several types of noise are typically used, namely Uniform White Noise, Gaussian White Noise, and Periodic Random Noise.

The term white in the definition of noise refers to the frequency domain characteristic of noise. Ideal white noise has equal power per unit bandwidth, resulting in a flat power spectral density across the frequency range of interest. Thus, the power in the frequency range from 100 Hz to

Chapter 17 Signal Generation

110 Hz is the same as the power in the frequency range from 1000 Hz to 1010 Hz. In practical measurements, to achieve the flat power spectral density would require an infinite number of samples. Thus, when making measurements of white noise, the power spectra are usually averaged, with more number of averages resulting in a flatter power spectrum.

The terms uniform and Gaussian refer to the probability density function (PDF) of the amplitudes of the time domain samples of the noise. For uniform white noise, the PDF of the amplitudes of the time domain samples is uniform within the specified maximum and minimum levels. Another way to state this is to say that all amplitude values between some limits are equally likely or probable. Thermal noise produced in active components tends to be uniform white in distribution. Figure 17-5 shows the distribution of the samples of uniform white noise.

Figure 17-5. Uniform White Noise

For Gaussian white noise, the PDF of the amplitudes of the time domain samples is Gaussian. If uniform white noise is passed through a linear system, the resulting output will be Gaussian white noise. Figure 17-6 shows the distribution of the samples of Gaussian white noise.

Chapter 17 Signal Generation

Figure 17-6. Gaussian White Noise

Periodic Random Noise (PRN) is a summation of sinusoidal signals with the same amplitudes but with random phases. It consists of all sine waves with frequencies that can be represented with an integral number of cycles in the requested number of samples. Since PRN contains only integral-cycle sinusoids, you do not need to window PRN before performing spectral analysis because PRN is self-windowing and therefore has no spectral leakage.

PRN does not have energy at all frequencies, as white noise does, but only at discrete frequencies which correspond to harmonics of a fundamental frequency which is equal to the sampling frequency divided by the number of samples. However, the level of noise at each of the discrete frequencies is the same.

PRN can be used to compute the frequency response of a linear system with one time record instead of averaging the frequency response over several time records, as you must for nonperiodic random noise sources.

Figure 17-7 shows the spectrum of periodic random noise and the averaged spectra of white noise.

Chapter 17 Signal Generation

Figure 17-7. Spectral Representation of Periodic Random Noise and

Averaged White Noise

Part IV

Instrument Control in LabVIEW

This part explains how to control instruments in LabVIEW.

Part IV, Instrument Control in LabVIEW, contains the following chapters:

•Chapter 18, Using LabVIEW to Control Instruments, introduces LabVIEW as a way to control instruments.

•Chapter 19, Instrument Drivers in LabVIEW, explains what instrument drivers are, where to find them, and how to use them.

•Chapter 20, VISA in LabVIEW, explains the basic concepts of VISA in LabVIEW.