Apple

A filter's transfer function simultaneously describes its response to a one-sample impulse and its response to any complex frequency in the z-domain. There's no need to compromise.
The reason for this? Applying a filter to a signal is the same as convolving the signal by the filter's impulse response. Convolution in the time domain, as exemplified by filters, is identical to multiplication in the frequency domain. Thus we can look at any point in the transfer function (as evaluated in the z-domain) and derive the effect the described filter will have on that frequency.

To expand on that: When we graph the filter response, the transfer function is what's getting graphed. A magnitude chart depicts the logarithm of the transfer function's magnitude for e^(iw) where w is angular frequency; a phase chart depicts the imaginary part of the logarithm.

References:
	>Re: Filter response curve (From: Roman Thilenius <email@hidden>)
	>Re: Filter response curve (From: Evan Balster <email@hidden>)