Hack Audio by Eric Tarr

Author:Eric Tarr
Language: eng
Format: epub, pdf
Publisher: Taylor & Francis (CAM)
Published: 2018-06-07T16:00:00+00:00

Sine Wave Analysis

One method to analyze the behavior of a system is to use a sine wave as an input signal. In this case, the behavior of a system is analyzed at an individual frequency.

Consider the LPF in Figure 12.3 for a 1 Hz sine wave input signal. As an example, assume a sampling rate of . The number of samples per cycle for a 1 Hz sine wave is:

In this system, the input signal is added together with the input signal after a one-sample delay. For an input signal which completes a cycle after 48,000 samples, there is a negligible phase difference between the delayed signal and the unprocessed signal. In other words, this system creates constructive interference for the 1 Hz input signal (i.e., low frequencies). When the two signal paths are combined at the output, the amplitude of the input signal essentially doubles, or increases by ~6 dB.

As a contrast, consider a high-frequency sine wave as the input signal. For this sampling rate, the Nyquist frequency is 24,000 Hz. The number of samples per cycle for a 24,000 Hz sine wave is:

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