Audio Signal Processing: changing spectrum directly

In summary, the author is having trouble understanding the consequences of directly changing the frequencies in the spectrum of an audio signal. He gives an example of adding zeros to the end of the spectrum to create a doubled number of samples, and then transforming back into the time domain. He explains that both experiments have different consequences, with the first experiment doubling the signal duration but slowing it down, and the second experiment reversing the order of the original audio samples.
  • #1
Evertje
9
0
Hi all,

I'm having some trouble understanding the consequences of directly changing the frequencies in the spectrum of an audio signal. Let me give you an example:

Let's say I have some audio signal, which I convert to a spectrum (in LabView, using a
direct cosine transform (to avoid explicitly working with phases)). Then, when I have this
spectrum, I add a bunch of zeroes to the end (so that I exactly double the number of
samples). Now, since I've double the number of samples, my audio signal becomes twice
as long (same playback rate), and my sound has changed pitch. The problem with this is,
I don't see how the inverse transform exactly "strechtes'' the time signal.

Now, starting with the original spectrum again, I try to interleave the spectrum with zeroes (i.e. sample1, 0, sample2, 0, etc..). So the spectrum again becomes twice
as long, and so does my audio sample. But, my audio sample now has not changed pitch/speed,
and furthermore, the sample now contains the original twice! The second part is in
reverse, however...

I have been trying for some time to figure it out; In the process i have learned a great deal about phase vocoders etc. and all kinds of techniques to change pitch w/o changing speed and vice versa. Maybe I'm missing a crucial part of 'understanding'. I am also unable to link this to the frequency resolution. Since i know that
Freq.Res = 1/(Num.Samp. * dt),
increasing the number of samples also increases my freq. res.; But this has "no effect" if I increase the number of samples in the frequency domain, right?
 
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  • #2
Interleaving frequency spectra (audio)

Hi,

I have an audio signal, which I have transformed into the frequency domain. Let's say for simplicity that it contains 1024 samples, sampled at 1024 Samples/s. Now, as a first experiment I add 1024 samples (in the frequency domain!), all with zero amplitude. This has doubled the number of samples. When I transform this spectrum back into the time domain, my signal lasts twice as long (I expected this), but my signal is slowed down by a factor of two also. I would've guessed this based on the fact that the time domain signal will not contain zeroes also.. but I do not see how the inverse transform also 'stretches' the time signal so that it exactly fits twice.

The second experiment involves not adding the zeros to the end of the spectrum, but interleaving them. Again, my signal duration doubles, but now something completely different
happens. In the time domain, the signal first plays normally, but the second half of my audio sample now contains the original in reverse!

I have the feeling I'm missing something crucial.. I am not changing the frequency resolution by adding zeroes in the frequency domain, am I?

Thanks for any help in advance!
 
  • #3


I can provide some insights on this topic. Directly changing the frequencies in the spectrum of an audio signal can have both positive and negative consequences. On one hand, it can allow for easy manipulation of pitch and time without changing the sound quality. On the other hand, it can also lead to artifacts and distortions in the audio signal.

In the example given, doubling the number of samples in the spectrum will indeed change the pitch of the audio signal, but it may also introduce unwanted artifacts due to the added zeroes. The inverse transform may not exactly "stretch" the time signal because it is not a linear process and the added zeroes can affect the overall shape of the signal.

Interleaving the spectrum with zeroes may seem like a solution, but it can also lead to issues such as aliasing and phase inconsistencies. This is because the spectrum and the time domain are not directly interchangeable and any manipulation in one domain will affect the other.

The concept of frequency resolution is also important to consider. Increasing the number of samples in the frequency domain does increase the frequency resolution, but it also introduces more data points and can lead to computational challenges. It is important to find a balance between frequency resolution and computational efficiency.

In summary, directly changing the spectrum of an audio signal can be a useful tool in signal processing, but it should be done with caution and with an understanding of the potential consequences. It is important to consider the relationship between the frequency and time domains and to find a balance between frequency resolution and computational efficiency.
 

1. What is Audio Signal Processing?

Audio Signal Processing is the manipulation and modification of audio signals using mathematical algorithms. It involves analyzing and changing the characteristics of an audio signal to achieve a desired outcome, such as improving sound quality or removing unwanted noise.

2. How does Audio Signal Processing work?

Audio Signal Processing works by converting analog audio signals into digital signals, which can then be manipulated using various mathematical techniques. These techniques include filtering, equalization, compression, and time/frequency domain transformations, among others.

3. What is the purpose of changing the spectrum directly in Audio Signal Processing?

Changing the spectrum directly in Audio Signal Processing allows for precise control over the frequency content of an audio signal. This can be useful for tasks such as removing unwanted frequencies or enhancing specific frequency ranges to improve sound quality.

4. What are some common applications of Audio Signal Processing?

Audio Signal Processing has a wide range of applications, including audio editing and mixing, noise reduction, speech recognition, and audio effects processing. It is also used in various fields such as telecommunications, music production, and biomedical engineering.

5. What are the benefits of using Audio Signal Processing?

The benefits of using Audio Signal Processing include improved sound quality, increased control over audio signals, and the ability to automate and streamline audio processing tasks. It also allows for the creation of innovative and complex audio effects that would not be possible using traditional methods.

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