UploadFile_6417

592 Chapter 10 ROUND-OFF EFFECTS IN DIGITAL FILTERS
P10.13 Let the system be given by y(n) =ay(n − 1) + x(n). Let a =0.7, which is quantized to B
(fractional) bits in the filter realization. Let the input sequence be x(n) =sin(n/11),
which is properly scaled to avoid overflow in the adder and quantized to B bits prior to
filtering. The multiplications in the filtering operations are also quantized to B bits.
1. Let B =5.Generate 100,000 samples of x(n), and filter through the system with
multiplication quantization. Compute the true output, the quantized output, the
output error, and the output SNR. Provide a plot of normalized histogram, and
comment on the results.
2. Let B = 10. Generate 100,000 samples of x(n) and filter through the system with
multiplication quantization. Compute the true output, the quantized output, the
output error, and the output SNR. Provide a plot of normalized histogram, and
comment on the results.
P10.14 Let the system be given by y(n) =ay(n − 1) + x(n). Let a =0.333, which is quantized to
B (fractional) bits in the filter realization. Let the input sequence be x(n) =sin(n/11),
which is properly scaled to avoid overflow in the adder and quantized to B bits prior to
filtering. The multiplications in the filtering operations are also quantized to B bits.
1. Let B =5.Generate 100,000 samples of x(n), and filter through the system with
multiplication quantization. Compute the true output, the quantized output, the
output error, and the output SNR. Provide a plot of normalized histogram and
comment on the results.
2. Let B = 10. Generate 100,000 samples of x(n), and filter through the system with
multiplication quantization. Compute the true output, the quantized output, the
output error, and the output SNR. Provide a plot of normalized histogram and
comment on the results.
P10.15 Consider the 2nd-order IIR filter given in (10.51) with r =0.8 and θ = π/4. The input to
this filter is x(n) =sin(n/23).
1. Investigate the multiplication quantization error behavior of this filter for B =5bits.
Determine the true output SNR, the computed output SNR, and the upper and
lower bounds of the SNR. Plot the normalized histogram of the output error.
2. Investigate the multiplication quantization error behavior of this filter for B =10
bits. Determine the true output SNR, the computed output SNR, and the upper and
lower bounds of the SNR. Plot the normalized histogram of the output error.
P10.16 Consider the second-order IIR filter given in (10.51) with r =0. − 8 and θ =2π/3. The
input to this filter is x(n) =sin(n/23).
1. Investigate the multiplication quantization error behavior of this filter for B =5bits.
Determine the true output SNR, the computed output SNR, and the upper and
lower bounds of the SNR. Plot the normalized histogram of the output error.
2. Investigate the multiplication quantization error behavior of this filter for B =10bits.
Determine the true output SNR, the computed output SNR, and the upper and
lower bounds of the SNR. Plot the normalized histogram of the output error.
P10.17 Consider a 5th-order FIR system given by
H(z) =0.1+0.2z −1 +0.3z −2 +0.3z −3 +0.2z −4 +0.1z −5
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.