single-bin DFT算法

single-bin DFT算法是一种可以计算单个频率分量的快速傅里叶变换（FFT）算法。它适用于需要对输入信号进行频域分析的应用。该算法利用了傅里叶变换的对称性质和周期性质，通过简单的数学运算即可计算出所需的单个频率分量。相比于传统的FFT算法，single-bin DFT算法的计算量和复杂度更低，因此更适用于实时系统和嵌入式系统等资源受限的环境。

相关问题

goertzel算法滤波matlab代码

### Goertzel Algorithm Filter Implementation in MATLAB

The Goertzel algorithm is an efficient method to compute one or a few frequency components of the discrete Fourier transform (DFT). This approach can be particularly useful when only specific frequencies need evaluation, as opposed to computing all DFT coefficients.

Below demonstrates how this technique may be implemented within MATLAB:

function result = goertzel_filter(x, f, fs)
% GOERTZEL_FILTER applies the Goertzel algorithm on input signal x at target frequency f with sampling rate fs.
    N = length(x);
    k = round(f * N / fs); % Calculate bin index corresponding to desired frequency
    
    coeff = 2 * cos(2*pi*k/N);
    
    q1 = 0;
    q2 = 0;

    for n = 1:N
        y = x(n) + coeff*q1 - q2;
        q2 = q1;
        q1 = y;
    end
    
    real_part = (q1 - q2*cos(2*pi*k/N));
    imag_part = q2*sin(2*pi*k/N);

    magnitude_squared = real_part^2 + imag_part^2; 

    result = sqrt(magnitude_squared)/N;
end

This function `goertzel_filter` takes three parameters: the time-domain data vector `x`, the targeted frequency component `f`, and the sample rate `fs`. It calculates the power spectral density value specifically around that given frequency using the Goertzel formulae[^1].

For applying such filtering effectively over certain ranges rather than single points, consider looping through multiple values of interest or modifying the above script accordingly based upon requirements.