A signal processing apparatus includes an oscillation circuit, an interpolation circuit, a matching filter, a high-pass filter and a timing recovery circuit. The oscillation circuit generates a clock signal. The interpolation circuit performs interpolation on an input signal according to the clock signal to generate an interpolation sample result. The matching filter demodulates the interpolation sample result to generate an output signal. The high-pass filter performs high-pass filtering on the interpolation sample result to generate a filtered result. The timing recovery circuit receives the filtered result, and performs timing recovery according to the filtered result.