Question E7F13:
What is the function of taps in a digital signal processing filter?  

Choices:  
A: To reduce excess signal pressure levels  
B: Provide access for debugging software  
C: Select the point at which baseband signals are generated  
D: Provide incremental signal delays for filter algorithms    

Correct Answer is  D: Provide incremental signal delays for filter algorithms  

To understand “taps” in DSP filters, think of a chain of one-sample delays. Each tap picks off a progressively delayed version of the input, multiplies it by a coefficient, and all are summed to form the output.

Why D is correct (Provide incremental signal delays for filter algorithms):
- In an FIR filter, taps are the points along a delay line that provide signals delayed by 1, 2, 3, … samples.
- Each tap output is multiplied by a coefficient and summed to implement convolution.
- This is exactly the “incremental delays” a DSP filter algorithm needs.

Key formulas:
- FIR convolution:
  $$y[n] = \sum_{k=0}^{M-1} h[k]\,x[n-k]$$
  where each term corresponds to a tap (a one-sample delay per increment in k).
- Z-domain form:
  $$H(z) = \sum_{k=0}^{M-1} h[k]\,z^{-k}$$
  where each tap is a power of $z^{-1}$ (one-sample delay).
- Group delay (linear-phase FIR):
  $$\tau_g \approx \frac{M-1}{2}\ \text{samples}$$
  More taps ⇒ greater latency but usually better selectivity.

Why the other choices are incorrect:
- A: “Reduce excess signal pressure levels” — “Signal pressure” is not a DSP filter concept; taps don’t specifically reduce “pressure” or amplitude by themselves.
- B: “Provide access for debugging software” — Taps are structural elements of the filter, not debugging points.
- C: “Select the point at which baseband signals are generated” — Baseband generation involves mixing/decimation, not the function of filter taps.

Rules of thumb:
- More taps (larger M) generally mean:
  - Sharper transition band and higher stopband attenuation.
  - More computation and more latency (about $(M-1)/2$ samples for linear-phase FIR).