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Unformatted text preview: 1 The Hong Kong University of Science and Technology Department of Electronic and Computer Engineering ELEC 212 Chapter 7: FIR Filter Design Techniques 2 09-10 Fall ELEC 212 FIR Filter Design Techniques FIR Filter Design ¡ FIR filters almost entirely restricted to discrete-time implementations ( unlike IIR implementations ) ¡ Design techniques for FIR filters are based on directly approximating the desired frequency response of the DT system ¡ Compared to IIR filters, FIR filters assume linear phase ¡ The transformation methods for IIR filter design cannot be used for FIR filter design ¡ The simplest method of FIR filter design is window method 3 09-10 Fall ELEC 212 FIR Filter Design Techniques Window Method for FIR Filter Design ¡ For FIR filter design, H ( e j ω ) of the designed FIR filter is required to approximate the frequency response H d ( e j ω ) of an ideal filter . That is, h [ n ] is required to approximate h d [ n ] , where ¡ In general, many idealized systems are defined by a piecewise- constant or piecewise-functional frequency response with discontinuities at the boundaries between bands (eg Ideal LPF) ¡ As a result, h d [ n ] is noncausal and infinitely long . Hence, we cannot use the previous equations to design FIR filter 4 09-10 Fall ELEC 212 FIR Filter Design Techniques Window Method for FIR Filter Design ¡ Can approximate the desired impulse response by truncating . It is the same as multiplying it by a window function of width M ¡ In frequency domain, windowing is the same as convolving the desired ideal transfer function with the window function (Periodic convolution) ¡ Basis of window design method: select window function that will modify the desired transfer function in such a way that the resulting filter transfer is close enough to the desired response ¡ What happens when M increases/decreases? ¡ What are some potential problems with this method? Smearing around discontinuities of ideal filter ] [ ] [ ] [ n w n h n h d = 5 09-10 Fall ELEC 212 FIR Filter Design Techniques Commonly Used Windows Different windows have different tradeoffs in terms of width of main-lobe and height of side-lobes 6 09-10 Fall ELEC 212 FIR Filter Design Techniques Commonly Used Windows dB below main peak 7 09-10 Fall ELEC 212 FIR Filter Design Techniques Commonly Used Windows ¡ Windows with small side lobes yield better approximations of the ideal response ( ie less error in passband and stopband ), – seen from the second and fourth columns of Table 7.1 ¡ Windows with smaller main lobe width have narrower transition regions for given M – seen from third column of Table 7.1 ¡ Width of main lobe can be controlled by varying the window length M – height of side lobes are independent of M ¡ By choosing the appropriate shape and duration of the window, we can control the properties of the resulting FIR filter. However, trying different windows and adjusting lengths by trial and error is not always a satisfactory way ¡ A simple...
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