idft

Builtin index · Signal processing

result = idft(X)

Input: X · Output: result

What it is

X is a length-N complex vector (CVec).

Overloads

One call shape — this function is not overloaded.

Code	Input	Output	Description
`result = idft(X)`	`X` vector or CVecnot documented yet	`result` CVec	Returns a length-N `CVec`. Inverse of `dft`, same O(n²) direct implementation.

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

fs = 1000
n = 0:1:63
t = n / fs
x = sin(2*pi*100*t)

X = fft(x)
xr = idft(X)
print("idft roundtrip max err: {max(abs(xr - x))}")

k100 = 100 * length(x) / fs        # bin index equivalent to 100 Hz

bin100 = goertzel(x, k100)
print("goertzel magnitude at bin {k100}: {abs(bin100)}")
same = goertzel_freq(x, fs, 100)   # the Hz-parameterized convenience form

print("goertzel_freq agrees: {abs(same - bin100) < 1e-9}")

half = rfft(x)
back = irfft(half, 64)
print("rfft/irfft roundtrip max err: {max(abs(back - x))}")

output

idft roundtrip max err: 1.604386e-14
goertzel magnitude at bin 6.4: 32.158025
goertzel_freq agrees: true
rfft/irfft roundtrip max err: 3.330669e-16

from signal-processing