Lyons, Richard G - Understanding Digital Signal Processing
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Lyons, Richard G - Understanding Digital Signal Processing


DisciplinaProcessamento Digital de Sinais1.103 materiais4.182 seguidores
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the end of a lowpass filter\u2019s passband to be at 250 Hz, the 
beginning of the stopband is 350 Hz, and we need a stopband attenuation of 48 dB. Applying those values to 
Eq. (5-49), we have
(5-50)
Taking the integer closest to 21.8, i.e., 22, we then state that the lowpass filter in 
Figure 5-52 can be built using a 22-tap FIR filter. We\u2019ll use Eq. (5-49) many times in later chapters of this 
book.
References
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Chapter 5 Problems
5.1 We first introduced the notion of 
impulse response in Chapter 1, and here in Chapter 5 we discussed the importance of knowing the impulse 
response of FIR filter networks. With that said, if the y(n) output of a discrete system is equal to the system\u2019
s x(n) input sequence:
(a) Draw the unit impulse response of such a system.
(b) Draw the block diagram (structure) of that system.
(c) What is the frequency magnitude response of such a system? Prove your answer.
5.2 Consider a simple analog signal defined by x(t) = cos(2\u3c0800t) shown in Figure P5-2. The FIR lowpass filter 
has a passband extending from \u2212400 Hz to +400 Hz, a passband gain of unity, a transition region width of 
20 Hz, and a stopband attenuation of 60 dB.
(a) Draw the spectral magnitude of x(n) showing all spectral components in the range of \u22122fs to +2fs.
(b) Draw the spectral magnitude of y(n) showing all spectral components in the range of \u22122fs to +2fs.
(c) What is the time-domain peak amplitude of the sinusoidal y(n) output?
Figure P5-2
5.3 Assume we want to filter the audio signal from a digital video disc (DVD) player as shown in 
Figure P5-3. The filtered audio signal drives, by way of a digital-to-analog (D/A) converter, a speaker. For the 
audio signal to have acceptable time synchronization with the video signal, video engineers have determined 
that the time delay of the filter must be no greater than 6×10\u22123 seconds. If the fs sample rate of the audio is 
48 kHz, what is the maximum number of taps in the FIR filter that will satisfy the time delay restriction? 
(Assume a linear-phase FIR filter, and zero time delay through the D/A converter.)
Figure P5-3
5.4 There are times when we want to build a lowpass filter and a highpass filter that are complementary. By 
\u201ccomplementary\u201d we mean that a highpass filter\u2019s passband covers the frequency range defined by a 
lowpass filter\u2019s stopband range. This idea is illustrated in 
Figure P5-4(a). An example of such filters is an audio system, shown in Figure P5-4(b), where the low-
frequency spectral components of an x(n) audio signal drive, by way of a digital-to-analog (D/A) converter, 
a low-frequency speaker (woofer). Likewise, the high-frequency spectral components of x(n) drive a high-
frequency speaker (tweeter). Audio enthusiasts call Figure P5-4(b) a \u201ccrossover\u201d network. Assuming that 
the lowpass filter is implemented with a 15-tap FIR filter whose hLow(k) coefficients are those in Figure P5-4
(c), the complementary highpass filter will have the coefficients shown in Figure P5-4(d). Highpass 
coefficients hHigh(k) are defined by
Figure P5-4
Here is the problem: Draw a block diagram of a system that performs the process in 
P5-4(b) where only the hLow(k)
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