Lab Handout

Analysis of an Over-Sampling DSP System

Implement and analyze a basic over-sampling DSP system that includes digital anti-aliasing and digital anti-imaging filters. The project is shown in block diagram form below:

The pseudo-analog signal is to emulate the following analog signal:

Notice that since the bandwidth of interest (W) is up to 500 Hz, the last 1 kHz sinusoid represents an unwanted signal component (noise.)

At various stages of the DSP system, generate frequency spectra of the signal, designated by S1, S2, S3, etc. Compare and contrast the spectra at these various stages by answering the questions posed below.

Procedure and Analysis

  1. Use the analog MATLAB m-file (instructor provided) to construct s(t). Use the following specifications to construct the pseudo-analog signal
  1. Length of the signal: 1000 ms
  2. Sampling rate: 64 kHz
  1. Create the over-sampled digital signal from the pseudo-analog signal using the instructor m-file sample. This is the “test signal” for further processing.
  1. Design a digital low-pass filter of order 500 with a Blackman window and a cutoff frequency of 500 Hz at the over-sampling rate. Use this filter to process the test signal in the blocks labeled “low-pass filter.”
  1. Process the test signal according to the block diagram above.
  1. Conduct a spectrum analysis of the test signal at various stages of processing. Include in the report graphs of the spectra of the signal as follows (use the instructor m-file dtft_demof). [Note: depending on the speed of your computer the DTFT computations can take time; be patient.]

Spectrum / Range – Hz / No. of freq. points / Fs
S1 / 0 to 1200 / 4000 / 16000
S2 / 0 to 1200 / 4000 / 1000
S3 / 0 to 3500 / 8000 / 16000
S4 / 0 to 3500 / 8000 / 1000
S5 / 0 to 3500 / 8000 / 16000
S6 / 0 to 3500 / 8000 / 16000
  1. Include in your report a discussion that addresses the following questions. (Concentrate on the presence or absenceand position of frequency components in the various spectra, not the amplitudes of the components.)
  2. Does S1 represent the expected spectrum of the input analog signal?
  3. Compare S1 and S2. Are they the same? If not, what do think causes them to be different?
  4. Compare S1 and S3. What change has occurred?
  5. Compare S3 and S4. What change has occurred and why?
  6. Compare S3 and S5. Are they the same? If not, what is the possible explanation of why they are different?
  7. Compare S5, S6, and S3. What has occurred in S6? Are S3 and S6 the same?
  8. Which low-pass filter would you call the “anti-aliasing filter” and which would you call the “anti-imaging filter?”

What to turn in:

  1. Spectral plots of the signals at points S1 through S6
  2. Brief answers to the questions in part 6