New answers tagged poles-zeros
2
One thing to consider when implementing an IIR filter, whatever the order, is quantization and limit cycles.
Let me show you with a quick example with your original filter
$y[n] = a*x[n]+(1-a)*y[n-1]$
Let a = 0.005 and say that we use 16-bit signed coefficients.
$a_{fixedpoint} = a * 32768 = 164$
Let's assume that the input and output are 16-bit ...
2
In particular, is the fixed point design more challenging for smaller a or larger a ?
Smaller is worse: the closer $a$ gets to $0$, the closer the pol movess to the unit circle and the more time domain ringing you have.
What are the main design considerations to think about ?
A first order low-pass IIR filter is relatively benign. The sum absolute sum ...
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It used to be that multiplication was a lot more expensive than addition or bitwise operations. For integer (and fixed point) implementation, this can be taken exploited like this:
When $a=1/2$ an extremely efficient implementation can be made with a single add and a single shift.
$$ y[n] = (x[n] + y[n-1]) >> 1 $$
Similarly, fractions with a power ...
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because even though it has more poles than zeros
WRONG. The Z-transform transfer function will always have equal number of poles and zeros. Your poles are at $z = -5/4$ and $z = 1/4$. Zeros are at $z = -1/2$ and $z = \infty$. Since ROC will always be concentric circle region without including poles, there are 3 possible ROC for the given transfer function.
$...
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Only the transfer function in z-transform never gives the stability of the system because multiple systems with the same z transform can have different ROC. So you need additional information about the signal like is it causal, non-causal, stable etc. You can have multiple ROCs here.
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Given this is a filter and not an oscillator the correct answer is
$$H(s) = K\frac{s+2\pi15e9}{(s+2\pi20e9)(s+2\pi20e9)}$$
unless further clarification is given that there are complex poles.
When poles and zeros are described to be at a particular frequency in Hz in relation to a filter implementation, it is actually describing a system with a real ...
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