Response is defined simple as the ratio of the size of the signal coming out of a system to the size of the signal going in. Thus it is a dimensionless quantity. Like many other ratio scales in speech, we often like to use decibels for response, since decibels are a convenient means for expressing a ratio scale in logarithmic form. The formula for response in dB is then

You need to find a way to excite the system with a sinusoidal input of known and variable frequency, and have a means for measuring the size of this signal going in and the size of the signal coming out. For an electrical system, you might use a voltmeter for this. You can then measure the output voltage and the input voltage, from these you can calculate the response in dB using the formaula above, and then this can be repeated for a range of different frequency sinusoids. A frequency response graph simply shows how this measured response changes with the frequency of the sinusoid.

When we talk about how a system changes a signal that passes through it we can do so in two ways. Firstly we can look at the waveform shape that went in and the waveform shape that came out. Since this involves looking at the waveform shape against time, this is called a 'time domain' study of the behaviour of a system. Unless the input signal is very simple: a pulse, say, or a sinusoid, the time domain description is not very useful. In particular it is hard to generalise from the time behaviour to make a prediction for how the system would behave with other shaped time waveforms. Thus we prefer a description of the operation of the system which plots the spectrum of the input signal, the spectrum of the output signal and the frequency response of the system. These graphs all have axes of frequency, and such an explanation is said to be a 'frequency domain' explanation. It is potentially more powerful than a time-domain explanation, since knowledge of the frequency response curve allows us to predict the output spectrum for any given input spectrum. The output is simply the input multiplied by the response.

We use 'bandwidth' to mean a region of the frequency response of the system where all the sinusoids pass through with roughly equal values of the response. The standard definition of 'roughly equla' is usually taken to be as 'within 3dB'. Thus to measure the bandwidth, we find the peak response of the system and find what limits of frequency are at just 3dB lower than this. This range in frequency from the upper frequency limit at 3dB below peak, to the lower frequencylimit at 3dB below peak is known as the bandwidth.