BIEN 425 Lecture 15 By the end of

BIEN 425 – 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: DAC ADC • It will introduce additional quantization noise and aliasing noise • Computationally intensive

Decimation • Decreasing sampling rate • f. M = fs/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 HM(z) • Where HM(f) = • y(k) = M

Intepolation • Increasing sampling rate • f. L = Lfs • Observe here we are using zero-padding

Effect in frequency domain • Observe XL(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 L • Where HL(f) = • y(k) = HL(z)

Example • Lecture 15. m

Rational sampling rate converter L HL(z) • fnew = (L/M)fs • Combine HL and HM to form H 0 HM(z) M

• Since HL and HM 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 HM(z) M G(z) M HM(z)