1. FIR Filter Design & Implementation
To fully design and implement a filter five steps are required:
(1) Filter specification
(2) Coefficient calculation
(3) Structure selection
(4) Simulation (optional)
(5) Implementation

2. Software Tools for Designing Filter
MATLAB provides some advanced tools for filters design
Signal Processing Tool (SPTool)
Filter Design (FDATool)
There are also some free software packages to design filters
Our main problem is how to implement the filter given the coefficients
So we will design FIR filters using the relatively simple method of Windowing -- write Matlab scripts

3. Lowpass Filter Specification

4. Window Method : Step 1
First stage of this method is to calculate the coefficients of the ideal filter.
This is calculated as follows:

5. Normalized Transition Width
Window Method : Step 2
Second stage of this method is to select a window function based on the passband or attenuation specifications, then determine the filter length based on the required width of the transition band
Window
Type
Normalized Transition Width
Passband
Ripple (dB)
Stopband
Attenuation (dB)
Rectangular
0.9/N
0.7416 21
Hanning
3.1/N
0.0546 44
Hamming
3.3/N
0.0194 53
Blackman
5.5/N
0.0017 74

6. Window Method : Step 2
The normalized transition bandwidth as listed in the table is defined as
Example: If we choose the Hamming window, and specify a transition band from 6kHz to 7kHz, with sampling frequency at 40kHz, then the filter order is calculated as

7. Window Method : Step 3
The third stage is to calculate the set of truncated or windowed impulse response coefficients, h[n]:
for

8. Using Matlab's fir1()
Instead of doing the design start from the ideal reponse, we shall use Matlab's fir1() function
We will design a FIR filter with the following specification
sampling frequency = 8000
passband edge frequency = 1200
stopband edge frequency = 1800
minimum stopband attenuation = 40 dB
By using the Hamming window, the stopband attenuation specification is met
By default, fir1() uses the Hamming window
For more information, please refer to the Matlab on-line help

9. Using Matlab's fir1() fsamp = 8000; fp = 1200; % passband
fs = 1800; % stopband
fc = (fp+fs)/2; % cutoff
% default using Hamming window, compute order
N = round(3.3*fsamp/(fs-fp));
str=sprintf('Filter order = %d', N);
disp(str);
wc = 2*fc/fsamp; % normalize to pi radian
b=fir1(N,wc);
freqz(b,1,512,fsamp);
filtdesign.m

10. FIR Filter Structure - Direct Form

11. Linear Phase FIR
For linear phase FIR, such as those designed with the window method, the coefficients have to be symmetrical
We can then make use of the symmetry to reduce the multiplications

12. Example of Symmetrical FIR - Even Length

13. Example of Symmetrical FIR - Odd Length

14. FIR Filters Design with FDATool
The Filter Design and Analysis Tool (FDATool) is a graphical user interface (GUI) for designing, quantizing, and analyzing digital filters.
It includes a number of advanced filter design techniques and supports all the filter design methods in the Signal Processing Toolbox.
designing filters by setting filter specifications;
analyzing designed filters;
converting filters to different structures; and
quantizing and analyzing quantized filters.
Open the FDATool by typing "fdatool" at theMATLAB command window.