1. Zero-pad the input signals. Add an appropriate number of zeros to the end of each signal to ensure that their lengths are equivalent to the nearest power of 2. This step is crucial for the efficiency of the FFT algorithm.
2. Calculate the FFT of each input signal. Use the FFT algorithm to compute the discrete Fourier transform of each zero-padded signal. This results in two frequency-domain representations, $X_1(k)$ and $X_2(k)$, corresponding to the first and second input signals, respectively.
3. Perform element-wise multiplication in the frequency domain. Multiply the elements of the two transformed signals element-wise: $Y(k) = X_1(k) \cdot X_2(k)$. This multiplication represents the convolution of the two signals in the frequency domain.
4. Calculate the inverse FFT of the result. Apply the inverse FFT (IFFT) to the resulting frequency-domain signal $Y(k)$ to transform it back into the time domain. This yields the linear convolution of the two input signals.
5. Trim the result. Due to the zero-padding, the obtained signal might be longer than the actual convolution. Trim the excessive zeros from the beginning and the end of the result to retrieve the linear convolution in its original length.
By utilizing the properties of the DFT and the FFT algorithm, this approach transforms the convolution operation into element-wise multiplication in the frequency domain, making it computationally efficient for larger signal sizes.