Pink Noise or Impulse Response
In my limited experience, I've been interested in the differences I see in measuring response at the listening position depending on whether it's steady-state response using pink noise or impulse response transformed to the frequency domain. Anyone here have comments or links to help me understand this better?
I'm not sure I understand your question, but here I go.
Measuring frequency response of a system (an audio system in a room in this case) requires instrumentation with sufficiently wide bandwidth. Pink noise and impulse response are two ways of achieving wide bandwidth. Wiki mentions both of these methods (among others) in their entry on frequency response [1].
Pink noise [2] has a frequency spectrum that falls as 1/f, where f is the frequency. In pink noise, each octave carries an equal amount of noise power. For example, 20 to 40 Hz has the same power as 40 to 80 Hz. Ideal pink noise has infinite bandwidth and therefore is impossible to achieve.
An impulse [3] transformed to the frequency domain (that is, the frequency spectrum) has a spectrum that falls as 1/f^0, the power is constant with frequency. Each constant bandwidth section carries an equal amount of power. For example, 20 to 40 Hz has the same power as 40 to 60 Hz. Again, an ideal impulse response has infinite bandwidth and therefore is impossible to achieve.
But at audio frequencies, we can get good enough. From Wiki [3], "In practical systems, it is not possible to produce a perfect impulse to serve as input for testing; therefore, a brief pulse is sometimes used as an approximation of an impulse. Provided that the pulse is short enough compared to the impulse response, the result will be close to the true, theoretical, impulse response."
For example, an impulse can be approximate by a rectangle wave with a short pulse width. A rectangle wave has a frequency spectrum described by the square of the sinc function [4]. But for very short pulses the frequency spectrum is very flat over a wide range. For example, a rectangle wave with a pulse width of 2 microseconds has a frequency spectrum that is flat to within 0.1 dB from 20 Hz to 20 KHz.
Wiki is your friend.
[1]
Frequency response.
[2]
Pink noise, not to be confused with
Pink Floyd.
[3]
Impulse response. The first paragraph is not a very good description. Read further down under Mathematical considerations.
[4]
Sinc function.