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

DAC ADC

Decimation

• Decreasing sampling rate

• fM = fs/M

• Or simply taking every M samples (decimation)

• However, we will need to consider an anti-aliasing filter

)()( MkxkxM

Digital anti-aliasing filter• We can consider this as FIR filter

• Where HM(f) =

• y(k) =

HM(z) M

Intepolation

• Increasing sampling rate

• fL = Lfs

• Observe here we are using zero-padding

otherwise

LLkLkxkxL ,0

...2,,0),/()(

Effect in frequency domain

• Observe XL(f) = X(Lf)

• This means that frequency content is the power of xL(k) is 1/L times the original x(k)

• Need to compensate for the effect of 1/L in the anti-imaging filter

• Where HL(f) =

• y(k) =

L HL(z)

Example

• Lecture15.m

Rational sampling rate converter

L HL(z) HM(z) M

• fnew = (L/M)fs

• Combine HL and HM to form H0

• Since HL and HM are both LP

• H0(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) MMHM(z) HM(z)