Programmer Guide/Command Reference/EVAL/fft: Difference between revisions

Revision as of 14:55, 13 April 2011

Compute the discrete fourier transform of a real signal using the fft or the dft algorithm.

Usage 1

fft(n)

Usage 2

fft(x)

x: signal vector or matrix; if x is a matrix a spectrum of each column is computed

Result 2: A matrix y with ncol(x) columns and L+2 rows, where each column y[*,j] contains the complex spectrum of the column (channel) x[*,j]. The transformation length L is set to npow2(nrow(x)).

Usage 3

fft(x, n {, ytype, poffset, prange, aref})

x

signal vector or matrix; if x is a matrix a spectrum of each column is computed

n

desired length of analysis window;

If n < nrow(x), the analysis window length L is set to nrow(x), otherwise L is set to n.
If the analysis window length L is a power of 2 (L=2^M), the fft algorithm is used, otherwise the dft is used.
If L is greater than nrow(x), zero padding is applied to the signal.

ytype: select the type and format of the computed spectrum (default=0) → see Result 3
poffset: offset in samples to the signal begin or the selected zero phase position (default=0)

poffset=0	→ `phase[i] = atan2(im[i], re[i])`
otherwise	→ `phase[i] = (atan2(im[i], re[i]) - 2pii/L * poffset) % (2 * pi)`

prange=0	→ `0 <= phase[i] < 2*pi`
otherwise	→ `-pi <= phase[i] < pi`

aref: reference amplitude if the log. spectrum (ytype=4) is requested (default=1)

Result 3: A matrix y with ncol(x) columns, where each column y[*,j] contains the spectrum of the column (channel) x[*,j]. The type and the length of the spectra is selected by the argument ytype.

ytype	description	content of y[*,j]	nrow(y)
0	complex spectrum in cartesian format	`{ re₀, im₀, re₁, im₁, ... }`	L+2
1	complex spectrum in polar format	`{ amp₀, phase₀, amp₁, phase₁, ... } with: amp_i=sqrt(re_i² + im_i²), phase_i see poffset`	L+2
2	amplitude spectrum	`{ amp₀, amp₁, ... }`	L+1
3	power spectrum	`{ amp₀², amp₁², ... }`	L+1
4	logarithmic amplitude spectrum	`{ lev₀, lev₁, ... } with: lev_i=20*log₁₀(amp_i/aref)`	L+1

@@ Line 16: / Line 16: @@
 ::*If the analysis window length L is a power of 2 (L=2^M), the '''fft''' algorithm is used, otherwise the '''dft''' is used.
 ::*If L is greater than [[../nrow|nrow(''x'')]], zero padding is applied to the signal.
-:;<var>ytype</var>: select the type and format of the computed spectrum (default=0) -> see '''Result 3'''
+:;<var>ytype</var>: select the type and format of the computed spectrum (default=0) &rarr; see '''Result 3'''
 :;<var>poffset</var>: offset in samples to the signal begin or the selected ''zero phase'' position (default=0)
 :::{|class="keinrahmen"
-|''poffset''='''0''' ||-> <code>phase[i] = atan2(im[i], re[i])</code>
+|''poffset''='''0''' ||&rarr; <code>phase[i] = atan2(im[i], re[i])</code>
 |-
-|otherwise ||-> <code>phase[i] = (atan2(im[i], re[i]) - 2*pi*i/L * ''poffset'') % (2 * pi)</code>
+|otherwise ||&rarr; <code>phase[i] = (atan2(im[i], re[i]) - 2*pi*i/L * ''poffset'') % (2 * pi)</code>
 |}
 :;<var>prange</var>: selects the range of phase values (default=0)
 :::{|class="keinrahmen"
-|''prange''='''0''' ||-> <code>0 <= phase[i] < 2*pi</code>
+|''prange''='''0''' ||&rarr; <code>0 <= phase[i] < 2*pi</code>
 |-
-|otherwise ||-> <code>-pi <= phase[i] < pi</code>
+|otherwise ||&rarr; <code>-pi <= phase[i] < pi</code>
 |}
 :;<var>aref</var>: reference amplitude if the log. spectrum (''ytype''=4) is requested (default=1)