Question

Problem 5 (10 points): Circle "T" for True or "F" for False for each of the following statements T F For a smoothing filter given by y[n]-(1-a)x[n] + αy[n-1], where 0 < α 1, the effects of an individual input sample never die out. The following system, where N > 1, is a high-pass filter: TF N-1 T F If the output of a digital filter depends on both current and past input values, it is called T F An N-point moving average filter (where N > 1) can attenuate high frequency noise TFA filter given by y[n]-xIn] -x[n -1] can somewhat attenuate a DC offset but a recursive filter. better than an (N+2)-point moving average filter. cannot eliminate it completely.

Answer 1

Answers:

1. True. Note that current output y[n] depends on present input x[n] and immediate previous output y[n-1]. So the effect of an individual input sample does not really completely die down. It becomes smaller with each sampling interval but it is there theoretically.

2. False. This equation represents averaging of input over N samples. Averaging removes high frequency noise. Therefore this equation represents a low-pass filter.

3. False. If the current output of a digital filter is a function only of the present and past input samples then it is NOT a recursive filter. In general a recursive filter is the one where current output is a function of present and some of the past inputs AND some of the past outputs.

4. False. A filter length increases the smoothness of output also increases.

5. True. This assumes that offset is constant from sample-to-sample. A longer term average of samples gives a better idea of the offset then just considering two adjacent samples.

Hope this helps.