Filter design

The parameters required to design a filter are:

• Filter order(N), Filter type(Analog, Digital (FIR,IIR))
• Cut-off frequencies
• Stop-band ripple, pass-band ripple, stop-band attenuation
• transition bandwidth
• Gain

Filter design:

(1) Analog:

• Butterworth: Flat response is pass band and adequate roll-off (High roll-off)
• Chebyshev: Steeper roll-off but ripples in pass-band or stop-band
• Elliptic filters: Severe roll-off at the expense of ripple in both pass-band and stop-band (Low roll-off)
• Bessel filter: Has maximally flat group delay and has main application is audio cross-over. [What is cross-over? Ans: Most individual loud speaker drivers are incapable of covering the entire audio spectrum from low frequencies to high frequencies with acceptable relative volume and absence of distortion. Crossovers split the audio signal into separate frequency bands that can be separately routed to loudspeakers optimized for those bands]

(2) Digital:

• Digital: Bilinear transformation(Converting analog to digital filters) , window method, Frequency sampling.

Linear phase FIR filter types:

(1) Type-1: order = even; symmetricity = even;

• 1+Z^-1+Z^-2;
• 1+Z^-1+Z^-2+Z^-3+Z^-4;
• Any filter can be designed, most desired.

(2) Type-2: order = odd; symmetricity = even;

• 1+Z^-1
• Has zero at pi. Cannot design HPF.
• 1+Z^-1+Z^-2+Z^-3

(3) Type-3: order = even; symmetricity = odd;

• 1-Z^-2
• Has zeros at 0 and pi. Cannot design LPF,HPF and band reject filters
• 1+Z^-1-Z^-3-Z^-4
• Center co-efficient is always zero

(4) Type-4: order = odd; symmetricity = odd;

• 1-Z^-1
• Has zero at 0. Cannot design LPF.
• 1+Z^-1-Z^-2-Z^-3

Hilbert filters are designed of type-III and IV, why?

Highest power of Z is the order of the filter. Length is (Order+1).

Group delay = (order)/2;

Suppose a LPF filter designed to have cut-off frequency 8KHz to filter a signal with sampling frequency 64KHz, then when the same filter applied to a signal sampled at 256KHz will act as a filter having cut-off frequency 32KHz. (Similarly a half band filter will always filter out half of the band). so, a filter cut-off frequency is better specified in terms of normalized frequency.