N-1 | ||

Y(n) = | E | h(k)*x(n-k) |

k=0 |

The design of the actual filter can be broken down into five basic steps.

*Filter Specification*This may include stating the type of filter, for example lowpass filter, the desired amplitude and/or phase responses and the tolerances (if any) we are prepared to accept, the sampling frequency, and the wordlength of the input data.*Coefficient Calculation*At each step, we determine the coefficients of a transfer function H(z), which will satisfy the specifications given in (1). Our choice of coefficient calculation method will be influenced by several factors, the most important of which are the critical requirements in step (1).*Realization*This involves converting the transfer function obtained in (2) into a suitable filter network or structure.*Analysis of Finite Wordlength Effects*Here, we analyze the effect of quantizing the filter coefficients and the input data as well as the effect of carrying out the filtering operation using fixed wordlengths on the filter peformance.*Implementation*This involves producing the software code and/or hardware and performing the actual filtering.

**Windowing Functions**

WINDOW FUNCTION | TRANSITION WIDTH (NORMALIZED) | STOPBAND ATTENUATION IN (DB) | WINDOW FUNCTION W(N), |N|<=(N-1)/2 |
---|---|---|---|

Rectangular | .9/N | 21 | 1 |

Hanning | 3.1/N | 44 | .5+.5 cos((2*(PI)*n)/N) |

Hamming | 3.3/N | 53 | .54+.46 cos((2*(pi)*n)/N) |

Blackman | 5.5/N | 74 | .42+.5 cos((2*(pi)*n)/(N-1))+0.08 cos((4*(pi)*n)/(N-1)) |

**Ideal Impulse Response Functions**

Filter Type | Hd(n),n!=0 | Hd(0) |
---|---|---|

Lowpass | 2*fc*(sin (n*wc)/n*wc) | 2*fc |

Highpass | -2*fc*(sin (n*wc)/n*wc) | 1-2*fc |

Bandpass | 2*f2*(sin (n*w2)/n*w2)-2*f1*(sin (n*w1)/n*w1) | 2*(f2-f1) |

Bandstop | 2*f1*(sin (n*w1)/n*w1)-2*f2*(sin (n*w2)/n*w2) | 1-2*(f2-f1) |