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

Revision as of 13:06, 12 April 2011

Compute the forward or inverce discrete cosine transform (dct) of the input vector x. This function was implemented for the computation of the MFCC (mel-cepstrum coefficients)

Usage

dct(x {, n {, dir)

xthe data vector
n: the number of dct coefficients to compute or to use (default=nrow(x)); the meaning of this argument depends on the value of dir
dir: the direction of the dct (default=0)
{class="keinrahmen"

|dir=0 ||-> forward dct
|-
|otherwise ||-> inverse (or backward) dct

Result
A vector y containing the result of the transformation. In the following table NX is equal to nrow(x)



dir
n
dct-
length
y
nrow(y)
description


0

0 < n <= NX

NX

dct coefficients

n

forward dct; if n<NX only the first n coefficients are computed


1

0 < n <= NX

NX

data samples

NX

inverse dct; if n<NX only the first n coefficients of x are used (smoothing or liftering)


1

n > NX

n

data samples

n

inverse dct; the vector x is expanded with zeros to length n and the inverse transform is applied to the expanded vector (smoothing or liftering)

See also
fft, ifft, dft, cepstrum, lpc, complex arithmetic

<function list>

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:{{SUBPAGENAME}}}}
-=====dct=====
+Compute the forward or inverce '''discrete cosine transform''' (dct) of the input vector ''x''. This function was implemented for the computation of the MFCC (mel-cepstrum coefficients)
+;Usage:<code>dct(<var>x</var> {, <var>n</var> {, <var>dir</var>)</code>
+:;<var>x</var>the data vector
+:;<var>n</var>:the number of dct coefficients to compute or to use (default=<code>nrow(''x'')); the meaning of this argument depends on the value of ''dir''
+:;<var>dir</var>:the direction of the dct (default=0)
+:::{class="keinrahmen"
+|''dir''='''0''' ||-> forward dct
+|-
+|otherwise ||-> inverse (or backward) dct
+;Result: A vector ''y'' containing the result of the transformation. In the following table NX is equal to <code>nrow(''x'')</code>
+:{|class="einrahmen"
+!''dir'' !! ''n'' !! dct-<BR>length !! ''y'' !! nrow(''y'') !! description
+|-
+|'''0'''
+|<code>0 < ''n'' <= NX</code>
+|NX
+|dct coefficients
+|''n''
+|forward dct; if ''n''<NX only the first ''n'' coefficients are computed
+|-
+|'''1'''
+|<code>0 < ''n'' <= NX</code>
+|NX
+|data samples
+|NX
+|inverse dct; if ''n''<NX only the first ''n'' coefficients of ''x'' are used (smoothing or liftering)
+|-
+|'''1'''
+|<code>''n'' > NX</code>
+|''n''
+|data samples
+|''n''
+|inverse dct; the vector ''x'' is expanded with zeros to length ''n'' and the inverse transform is applied to the expanded vector (smoothing or liftering)
+|}
+;See also: [[Programmer_Guide/Command_Reference/EVAL/fft|fft]], [[Programmer_Guide/Command_Reference/EVAL/ifft|ifft]], [[Programmer_Guide/Command_Reference/EVAL/dft|dft]], [[Programmer_Guide/Command_Reference/EVAL/cepstrum|cepstrum]], [[Programmer_Guide/Command_Reference/EVAL/lpc|lpc]], [[Programmer_Guide/Command_Reference/EVAL/complex arithmetic|complex arithmetic]]
-Discrete Cosine Transform.
+[[Programmer_Guide/Command_Reference/EVAL#Functions|<function list>]]
-=====Usage:=====
-<code>dct(<var>x</var> {, n {, 0}})</code>
-=====Function:=====
-Computes the discrete cosine transform of <var>x</var>. <var>n</var> must be in the range <code>1..nrow(</code><var>x</var><code>)</code>. The default is <var>n</var> <code>= nrow(</code><var>x</var><code>)</code>.
-=====Result:=====
-A vector containing the first <var>n</var> dct coefficients.
-=====Usage:=====
-<code>dct(<var>x</var>, n, 1)</code>
-=====Function:=====
-Computes the inverse dct of <var>x</var>.
-If <var>n</var> <code><= nrow(</code><var>x</var><code>)</code>:
-Only the first <var>n</var> coefficients of <var>x</var> are used, the others are set to <code>0</code>. Output length = <code>nrow(</code><var>x</var><code>)</code>.
-If <var>n</var> <code>> nrow(</code><var>x</var><code>)</code>:
-<var>x</var> is expanded with zeros to <var>n</var> elements.
-=====Result:=====
-A vector containing the inverse dct.

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

Revision as of 13:06, 12 April 2011

Navigation menu

Page actions

Page actions

Personal tools

Navigation

Search

Tools

dir	n	dct- length	y	nrow(y)	description
0	`0 < n <= NX`	NX	dct coefficients	n	forward dct; if n<NX only the first n coefficients are computed
1	`0 < n <= NX`	NX	data samples	NX	inverse dct; if n<NX only the first n coefficients of x are used (smoothing or liftering)
1	`n > NX`	n	data samples	n	inverse dct; the vector x is expanded with zeros to length n and the inverse transform is applied to the expanded vector (smoothing or liftering)