There are few methods to design the FIR filters. One of the most common methods because of its simple and analytical nature is to start with a box type ideal low pass filter in the frequency domain with a specific cut of frequency Fc and transforming this ideal filter to the time domain and then descretize the time in units of the sampling time Ts. Fc/Fs must be much smaller than one half. If the frequency is > Fs/2 aliasing distortion will occur. Transforming an ideal low pass filter in time domain results in sin x/ x function. This function represents the the impulse response of the filter h[t]. since the sinc function extends to infinity in both side, it results in an infinite numbers of taps of the FIR filters. Then such filters are not practical and the number of taps must be truncated. This is accomplished by using windows. The simplest window is the rectangular window. But this window has small stop band attenuation for the same number of taps. There are may types of windows to achieve the required top band attenuation. It is so that as the stop band attenuation increases the transition region from pass band to stop band increases.
S0, windows are used to shape the response of the filter. Consequently, more or less filter windows are determined by required stop band attenuation
Please for much more details revert to the book in Link:
The choice of the window depends on the noise characteristics, transition region and the number of coefficients required. I think you will find enough guidance on this matter in any standard DSP text.
The window design technique allows us to utilize the design techniques already formulated for the IIR case rather than deriving new methods for the FIR case separately.
There are few methods to design the FIR filters. One of the most common methods because of its simple and analytical nature is to start with a box type ideal low pass filter in the frequency domain with a specific cut of frequency Fc and transforming this ideal filter to the time domain and then descretize the time in units of the sampling time Ts. Fc/Fs must be much smaller than one half. If the frequency is > Fs/2 aliasing distortion will occur. Transforming an ideal low pass filter in time domain results in sin x/ x function. This function represents the the impulse response of the filter h[t]. since the sinc function extends to infinity in both side, it results in an infinite numbers of taps of the FIR filters. Then such filters are not practical and the number of taps must be truncated. This is accomplished by using windows. The simplest window is the rectangular window. But this window has small stop band attenuation for the same number of taps. There are may types of windows to achieve the required top band attenuation. It is so that as the stop band attenuation increases the transition region from pass band to stop band increases.
S0, windows are used to shape the response of the filter. Consequently, more or less filter windows are determined by required stop band attenuation
Please for much more details revert to the book in Link:
FIR filter design essentially consists of two parts
(i) approximation problem
(ii) realization problem
The approximation stage takes the specification and gives a transfer function using some method or algorithm to find the best filter transfer function.
The realization part deals with choosing the structure to implement the transfer function which may be in the form of circuit diagram or in the form of a program.
There are essentially three well-known methods for FIR filter design namely:
(1) The window method
(2) The frequency sampling technique
(3) Optimal filter design methods
Of the above three the major advantages of using window method is their relative simplicity as compared to other methods and ease of use.(So are more popular).The fact that well defined equations are often available for calculating the window coefficients has made this method successful.
The basic idea behind the window design it to choose a proper ideal frequency-selective filter(which always has a non causal, infinite-duration impulse response) and then to truncate ( or window) its impulse response to obtain a linear-phase and causal FIR filter.
The Bartlett window reduces the overshoot in the designed filter but spreads the transition region considerably. The Hanning, Hamming and Blackman windows use progressively more complicated cosine functions to provide a smooth truncation of the ideal impulse response and a frequency response that looks better. The best window results probably come from using the Kaiser window, which has a parameter ß that allows adjustment of the compromise between the overshoot reduction and transition region width spreading.
It is not the only method to design FIR filters. The best known methods are.
1.- Window design method.
2.- Frequency Sampling method
3.- Weighted least squares design
4.- Equiripple FIR filters, in the time and frequency domain.
The window method is based on calculating the impulse response of an ideal digital filter, which is IIR, and on using a window to obtain a finite impulse response. The characteristics of the FIR filter depends on the chosen window. One of the most interesting properties you can get is linear phase. It is explained in many DSP books.
Frequency sampling methods only guarantee good approximation to the desired response in some frequency values. The approximation in other values can be very bad.
Optimum equiripple linear phase filters is a good alternative. The procedure nds the impulse response that minimizes the maximum weighted error between the desired response and the actual response.
Your main question is "Why do we prefer window techniques compared to other techniques for FIR Filter design?". Probably, because of the simplicity in the design, and because the design method is very well understood with basic DSP knowledge. Also, you can get good results for many applications. But you must also considere Optimum equiripple linear phase filters.
Using Fourier series, abrupt truncation of filter coefficients to finite length results in ringing trails in the frequency response of FIR filter. In order to minimize the side lobe level or ringing trails we go for windowing technique.
Hamming window is the best technique, usually preferred by many others