EE3TR4 Lab 1: Fourier Analysis

Room: lab- ITB157

Please work in pairs. The final report (one per pair) is due Monday Feb. 11 2008 in the ITB printer room (assignment box for EE3tr4) by 4:00pm. Please note that each group is expected to work independently. Please be familiar with the guidelines on academic integrity, summarized on the course outline available on the web. One lab report per group.

This lab is project based, consisting of two parts. The first part is a theoretical analysis and a computer simulation of the output of a filter. These theoretical results are then compared with actual measurements you get in the lab. As such, this project involves going to the lab during your regular lab session to gather experimental results.

The second part involves listening to various forms of filtered speech. The idea is to try to figure out why the filtered speech sounds as it does.

Part I: Filter Analysis

The objective of this lab is to compare theoretical predictions and experimental measurements of the output of a filter, driven by a function generator, as shown in Figure 1. This comparison is in both the time and frequency domains. You can use a second-order low-pass Butterworth filter with a cutoff frequency of 1.591 KHz. Its circuit diagram for this filter is shown in Figure 2.

Figure 1. Configuration of filtering operation

The transfer function H(ω) for the second-order Butterworth low-pass filter is given as

where s = jω, ω₀ = 2πf₀, and f₀ is the cutoff frequency in Hertz, equal to 1.591Khz for the circuit of Figure 2.

The scopes available in the lab have a frequency-domain (FFT) display, which shows only the magnitude spectrum of the signal applied to the input of the instrument. The file “fft_operations.pdf” (on the website) explains how to use this display. A few tips on the settings to use are included in the appendix of this document. Note that with these scopes, you can dump the screen to a PC-compatible floppy disk. Therefore, you should bring a formatted floppy with you to the lab. Information on saving the screen to a floppy is given in the file “saving_to_floppy.pdf” (also available on the website).

Both theory and experiment should be completed in both the time and frequency domains. Here are some suggestions for the frequency domain. You are welcome to try other experiments. The theoretical analysis would be greatly enhanced by a computer program, preferably in Matlab.

• Calculate the magnitude and phase responses of the filter using the above equation and compare them to measurement
• Calculate the spectrum of the filter input and output, using e.g., a square wave input signal with frequency 500 Hz. Compare these calculations with measurement. Convert the spectrum of the output waveform into the time domain. (This can be done using the FFT function in Matlab). Compare with what you see on the scope.

Here are some suggestions for the time domain analysis:

• Evaluate the impulse response of the filter. This can be done using the IFFT command in Matlab, knowing the frequency response.
• The output waveform can be evaluated by the convolution of the filter impulse response with the input signal. This can be implemented using the Matlab CONV function. To get meaningful results with this function, the first and last L_h -1 samples of the output must be discarded, since these correspond to the transients of the convolution.. Here, L_h is the truncated length of the impulse response.

Part II: Speech Filtering

This should be a bit more fun than part I. On the computers in the lab, run the matlab program “filtDemo”. It plays speech that has been passed through various forms of filter. Plots of the input and output spectra are shown on the displays. Note especially how the notch filter can suppress the sinusoidal tone. Pay attention to the difference in sound of the outputs of each type of filter. Why do the outputs sound different from the original input speech?

APPENDIX – Tips on Using the FFT facility on the Scopes

Set the “window” soft key to “Hanning”.

The frequency scan need not be greater than 10 kHz. This will show the first 20 harmonics of the signal.

The frequency domain display will appear as a sequence of spikes. Measure their frequency and their corresponding amplitude values (note the amplitude scale is in dB).

When measuring the signal at the output of the low-pass filter, note that the higher-frequency components of the signal are significantly suppressed at the output, relative to the input, by the low-pass filter. This is what causes the output waveform to be significantly different from that at the input.