For the structure shown below. (a) Define the limits of the high pass filter in
ID: 2082951 • Letter: F
Question
For the structure shown below. (a) Define the limits of the high pass filter in the structure with respect to the cut-off frequency of the high pass filter, omega_c, and plot the ideal magnitude response of the high pass filter clearly showing all parameters. (b) If the high pass filter in the structure shown below, has a cutoff frequency omega_c, prove that the magnitude response of the structure shown below, is that of a lowpass filter. (c) Plot the magnitude response of resulting filter at the output with all the parameters.Explanation / Answer
Finite Word Length Effects in IIR Filters
In general IIR filters are much more difficult to analyse than FIR filters because of the feedback structure. However,
both types of filter suffer from the same problems and have the same sources of noise due to finite word length effects.
The extent of filter degradation depends on the length of the word and the type of arithmetic (fixed or floating point)
used to perform the filtering operation. A summary of the main four sources of noise and their corresponding effects on
IIR filter performance are summarised in Table 5.1.
Source of noise
Affect on performance
Reduction techniques
A/D conversion.
Quantisation noise =
q
2
/12.
•
Increase number of bits.
•
Use multirate techniques.
Arithmetic round off.
Causes low level limit cycles i.e.
oscillations at the filter output, or
output stuck at a nonzero value,
even when there is no input.
•
Use double word length for
intermediate results.
•
Optimise filter structure to
include error spectral shaping.
•
Add a dither signal before
rounding.
Coefficient quantisation.
Modifies position of the poles and
zeros, may cause instability and a
change in the frequency response.
•
Use sufficient Nos. of bits in
fixed-point representation.
•
Optimise selection of filter
coefficients.
•
Use floating-point arithmetic.
Arithmetic overflow.
Incorrect output signal.
•
Scale filter coefficients (at cost
of reduced SNR).
•
Detect and use “maximum”
rather than “overflowed” value.
•
Use floating-point arithm
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