Folks:

Just to make sure, when I ask for a sine wave of frequency 0.8*pi in the first part of the homework, I mean a sine wave whose frequency is 0.8 of the Nyquist frequency.

If you plot the signal, you should see a high frequency-looking thing.

Tom

Sunday, 15 March 1998

Generally:

This assignment was quite nicely done. The most common problems were getting the frequency axis wrong for the subsampled signal in part 1, and plotting deviation as the log of the difference between frequency responses.

Part 1:

Some folks, having forgotten that the new sampling frequency was 4000 Hz after subsampling, managed to explain why it was that the sine component at 400 Hz 'moved' to 800 Hz (it doesn't). The 3200 Hz component is aliased down to 800 Hz. Note: the correct term is 'aliasing', not 'folding' or anything else. You had to mention aliasing to get full credit for this question.

Part 2:

The filter's impulse response is real because its frequency response is conjugate symmetric - it has nothing to do with the frequency response being real, or with the filter being zero-phase. The Hanning filter is actually worse from an MSE point of view, but does not have any ripples.

My biggest beef with the various descriptions of what was going on was the mention of the ripple/transition width tradeoff, or the assertion that the truncated filter had a narrower transition band. Since the filter has no stopband, it cannot have a transition width. Don't blindly state what's in the notes about windowed filter design because it doesn't always apply! We weren't trying to design a lowpass filter.

The correct way to compute deviation is as the difference between the logged magnitudes of the ideal and non-ideal filters, i.e. something like DEV = 20*log10(abs(ideal)) - 20*log10(abs(actual)), NOT by logging the difference. A dB scale is unitless - you can ONLY take dB's of a ratio. In this case, of course, finding the difference of the logs is equivalent to finding the log of the quotient, which is dimensionless. Finding the dB of a difference makes no sense.

Please get the solution code from the Web or the ftp site. The written-up solution is posted on the Web too.

Tom