为初学者实现实时频谱
我想开发一个应用程序，它将音频（.wav）作为输入并显示其实时同步频谱。从我对这个主题的看法来看，这需要对波进行傅里叶变换。有人可以建议我应该从哪里开始吗？可能的参考资料和书籍。我想学习实时频谱实现的细节，而不是我非常熟悉的GUI的开发（C#和C++）。
I want to develop an application that would take audio(.wav) as input and display its real time simultaneous frequency spectrum . From what i have looked upon the subject , this requires fourier transform of the waves . Can someone suggest where i should start with ? Possible references and books . I want to learn the details of the implementations of realtime frequency spetrum rather than the development of GUI which i am quite familiar with(in C# and in C++).
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已经有很多库可以为您执行 FFT。没有理由重新发明轮子。 DirectX 有一个 实现，但它可能只出现在最新版本中。 这里是一个开源 C 库。
如果您想了解其背后的数学原理，这里有一个简单的解释和这里有一个复杂的解释解释。
There are already many libraries to do FFTs for you. No reason to reinvent the wheel. DirectX has an implementation but it might only be in the most recent version. Here's an open source C library for it.
If you want to understand the math behind it, here's a simple explanation and here's a complicated explanation.
看看 FFTW。
就书籍而言，关于信号处理的经典教科书是奥本海姆和谢弗的《数字信号处理》。虽然是大学水平，但已经完全通过了。有些地方你确实需要一些微积分知识。
Take a look at FFTW.
As far as books go, the classic text book on signal processing is Oppenheim and Schafer's Digital Signal Processing. Its college level but it is quite through. You do need some knowledge of calculus in places.
您应该首先打开 wav 文件，提取音频流并对其进行解码。有第三方库可以帮助完成此操作。
You should begin with opening the wav file, extracting the audio stream and decoding it. There are 3rd party libraries to help on this operation.
在开始实施应用程序来显示某些内容之前，应该了解一些理论。这里有一些关于数字信号处理的免费在线资源，这是理解 FFT 和频谱以及如何不滥用它们的基础。
http://www.dspguide.com/pdfbook.htm
http://www.bores.com/courses/intro/index.htm
http://ccrma.stanford.edu/courses/320/Welcome.html
http://yehar.com/blog/?p=121/
One should understand a bit of the theory before going off and implementing an application to display something. Here are some free online resources on digital signal processing, which is the basis for understanding FFTs and frequency spectrums, and maybe how not to misuse them.
http://www.dspguide.com/pdfbook.htm
http://www.bores.com/courses/intro/index.htm
http://ccrma.stanford.edu/courses/320/Welcome.html
http://yehar.com/blog/?p=121/