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DSP.Filter.IIR.IIR | Portability | portable | Stability | experimental | Maintainer | m.p.donadio@ieee.org |
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Description |
IIR functions
IMPORTANT NOTE:
Except in integrator, we use the convention that
y[n] = sum(k=0..M) b_k*x[n-k] - sum(k=1..N) a_k*y[n-k] sum(k=0..M) b_k*z^-1 H(z) = ------------------------ 1 + sum(k=1..N) a_k*z^-1 |
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Synopsis |
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Documentation |
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integrator |
:: Num a | | => a | a
| -> [a] | x[n]
| -> [a] | y[n]
| This is an integrator when a==1, and a leaky integrator when 0 < a < 1.
y[n] = a * y[n-1] + x[n] |
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fos_df1 |
:: Num a | | => a | a_1
| -> a | b_0
| -> a | b_1
| -> [a] | x[n]
| -> [a] | y[n]
| First order section, DF1
v[n] = b0 * x[n] + b1 * x[n-1] y[n] = v[n] - a1 * y[n-1] |
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fos_df2 |
:: Num a | | => a | a_1
| -> a | b_0
| -> a | b_1
| -> [a] | x[n]
| -> [a] | y[n]
| First order section, DF2
w[n] = -a1 * w[n-1] + x[n] y[n] = b0 * w[n] + b1 * w[n-1] |
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fos_df2t |
:: Num a | | => a | a_1
| -> a | b_0
| -> a | b_1
| -> [a] | x[n]
| -> [a] | y[n]
| First order section, DF2T
v0[n] = b0 * x[n] + v1[n-1] y[n] = v0[n] v1[n] = -a1 * y[n] + b1 * x[n] |
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biquad_df1 |
:: Num a | | => a | a_1
| -> a | a_2
| -> a | b_0
| -> a | b_1
| -> a | b_2
| -> [a] | x[n]
| -> [a] | y[n]
| Direct Form I for a second order section
v[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] y[n] = v[n] - a1 * y[n-1] - a2 * y[n-2] |
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biquad_df2 |
:: Num a | | => a | a_1
| -> a | a_2
| -> a | b_0
| -> a | b_1
| -> a | b_2
| -> [a] | x[n]
| -> [a] | y[n]
| Direct Form II for a second order section (biquad)
w[n] = -a1 * w[n-1] - a2 * w[n-2] + x[n] y[n] = b0 * w[n] + b1 * w[n-1] + b2 * w[n-2] |
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biquad_df2t |
:: Num a | | => a | a_1
| -> a | a_2
| -> a | b_0
| -> a | b_1
| -> a | b_2
| -> [a] | x[n]
| -> [a] | y[n]
| Transposed Direct Form II for a second order section
v0[n] = b0 * x[n] + v1[n-1] y[n] = v0[n] v1[n] = -a1 * y[n] + b1 * x[n] + v2[n-1] v2[n] = -a2 * y[n] + b2 * x[n] |
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iir_df1 |
:: Num a | | => (Array Int a, Array Int a) | (b,a)
| -> [a] | x[n]
| -> [a] | y[n]
| Direct Form I IIR
v[n] = sum(k=0..M) b_k*x[n-k] y[n] = v[n] - sum(k=1..N) a_k*y[n-k] v[n] is calculated with fir
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iir_df2 |
:: Num a | | => (Array Int a, Array Int a) | (b,a)
| -> [a] | x[n]
| -> [a] | y[n]
| Direct Form II IIR
w[n] = x[n] - sum(k=1..N) a_k*w[n-k] y[n] = sum(k=0..M) b_k*w[n-k] |
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Produced by Haddock version 0.8 |