S-72.116 Signals and Systems (Signaalit ja järjestelmät)

Work 1

SIGNAL FREQUENCY ANALYSIS USING MATLAB

Preliminary assignments

Return the written preliminary report to the supervisor of the work in the beginning of your laboratory shift. Make a copy of your preliminary report and give it to the members of your group. In the report, write down your group's number, date, the names of all the group members and your student numbers. The preliminary report can also be done in Finnish or in Swedish.

1. What do the following concepts mean in the context of signals? Give examples about how these concepts associate with real signals. One example/concept is enough.

• Discrete-time
• Quantization
• Deterministic signal
• Stochastic signal
• DFT
• dBm

1. When it is particularly useful to examine the signal in time domain (in the form x(t)), and when would it be better to use the frequency domain (ie. X(f))? Give at least one example of both cases. Using pictures is recommended.

3. In the one-sided spectrum analysis of signal x(t) the following frequency components were observed in the 50 ohm system.

1. Change the frequency components' dBm-values to RMS-voltages and to peak-voltages. 0 dBm corresponds the power of 1mW to the load (to the systems's nominal impedance). The frequency components may be interpreted as cosine waves, when peak-value = Ö 2 * RMS-value.
2. On the basis of the previous results, form a mathematical formula for voltage signal x(t) based on the frequencies and cosine wave peak-values. The phase difference of all cosine waves is 0 radians.
3. Draw a one-sided peak-value spectrum (ie. frequency domain presentation X(f)) of signal x(t) based on the chart values and your calculations. Report proper scale names and values so that the results would be easily interpreted. Logarithmic scales are recommended. Also give the diagram a proper title.

1. What is the difference between DFT and FFT? Why is the DFT not used in computers until recently?
2. 5 seconds' sample of sound (maximum frequency 20 kHz) is recorded in the sample frequency 44100 Hz. Compare the amount of calculations needed to perform the Fourier-transforms (DFT vs. FFT).
3. If the calculation of FFT would take 350 MHz Pentium II -processor a minute, how long would it take to calculate the DFT using the same processor? 

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