[SciPy-User] 答复: Hilbert transform

[Tanguanzhong]

From the Scipy manual: It seems not complex signal but the real part of complex signal?

scipy.fftpack.hilbert(x)
 Return Hilbert transform of a periodic sequence x.

If x_j and y_j are Fourier coefficients of periodic functions x and y, respectively, then
  y_j = sqrt(-1)*sign(j) * x_j 

  y_0 = 0

Parameters
x : array_like
The input array, should be periodic.
_cache : dict, optional
Dictionary that contains the kernel used to do a convolution with.
Returns
y : ndarray
The transformed input.
Notes
If sum(x, axis=0) == 0 then hilbert(ihilbert(x)) == x.
For even len(x), the Nyquist mode of x is taken zero.
The sign of the returned transform does not have a factor -1 that is more often than not found in the definition
of the Hilbert transform.


BOBBY.TAN/tanguanzhong at huawei.com
 
发件人: scipy-user-bounces at scipy.org [mailto:scipy-user-bounces at scipy.org] 代表 Sturla Molden
发送时间: 2014年10月11日 23:16
收件人: scipy-user at scipy.org
主题: Re: [SciPy-User] Hilbert transform

Tanguanzhong <tanguanzhong at huawei.com> wrote:

> I have made a test for Hilbert transform for PCM data. Suggest 
> "pcmRawData" is PCM audio data and collect by pyaudio. After Hilbert 
> transform, "pcmData" has 90 degree phase shift relative to  "pcmRawData".

The Hilbert transform should return a complex signal, at least that is how it is defined.


Sturla

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