BIEN425 – Lecture 15 By the end of this lecture, you should be able to: –Design and implement integer decimators and interpolators –Design and implement a narrow band filter using interpolation and decimation techniques.

To resample a digital signal The simplest way: It will introduce additional quantization noise and aliasing noise Computationally intensive DACADC

Decimation Decreasing sampling rate f M = f s /M Or simply taking every M samples (decimation) However, we will need to consider an anti-aliasing filter

Digital anti-aliasing filter We can consider this as FIR filter Where H M (f) = y(k) = H M (z)M

Intepolation Increasing sampling rate f L = Lf s Observe here we are using zero-padding

Effect in frequency domain Observe X L (f) = X(Lf) This means that frequency content is the power of x L (k) is 1/L times the original x(k)

Need to compensate for the effect of 1/L in the anti- imaging filter Where H L (f) = y(k) = LH L (z)

Example Lecture15.m

Rational sampling rate converter LH L (z)H M (z)M f new = (L/M)f s Combine H L and H M to form H 0

Since H L and H M are both LP H 0 (f) = y(k)=

Narrow band filter Definition: sharp filter whose passband or stopband is small in comparison with sampling frequency Usually need high-order FIR filters Example: Ideal response

Reduce sampling rate by M Then create new filter G(f) Then interpolate by M again G(z)MMH M (z)