Time and Frequency Domain Analysis

A basic understanding of the relative strengths and differences between time- and frequency-domain analysis is critical to leveraging the measurement power presented in Smaart. The ability to examine a measurement from multiple perspectives is extremely useful in the process of analyzing a signal or system response. Each of Smaart’s primary operating modes (real-time and impulse response) includes both time- and frequency-domain measurement and analysis capability. 

The “domain” of a graph or signal refers to the independent variable, usually shown on the horizontal axis of a graph. Audio waveforms, for example, are time-domain signals, where the voltage or digital amplitude of the signal varies over time. Time is the independent variable in this case, so it normally goes on the (horizontal) x axis of a waveform graph, with amplitude on the (vertical) y axis. On a frequency-domain graph, we normally put frequency on the x axis and magnitude on the y axis. The exception in both cases is the spectrograph, which has two independent variables, so we orient it whichever direction makes the most sense in a given context.

 In recording applications, a time domain graph of an audio signal provides a view of the waveform – a critical view for sound editors. In sound system engineering and room acoustics, a time-domain view of system response (the impulse response) shows the propagation delay through the system and later arriving reflections and reverberation that could potentially be problematic. 

Frequency domain analysis of a signal provides a view of its spectrum, which is obviously an extremely useful set of information when analyzing tonal content or looking for feedback. A frequency domain view of system response (the transfer function or frequency response) provides an excellent look at the tonal response of a system as well as its time/phase response by frequency. 

The above graphic provides a very good example of the power of utilizing both time and frequency domain views for examining system response. The frequency response measurement depicts a response with a series of linearly spaced dips and peaks in its magnitude response (lower right). This ripple is a symptom of a problem however, and not the actual problem. The cause of the ripple is clearly identifiable in the timedomain view of the system response as an obvious second arrival in the impulse response, caused by a prominent reflection. Reflections are copies of the direct sound that arrive later in time, after bouncing off some surface. Mixing two copies of the same signal with a time offset between them results in the comb filter that we can see in the frequency domain view.