## Calculate Frequency of Kth Filter using Constant Q Spectral Transform

##### Definition:

Constant Q transform is closely associated into the Fourier transform.It converts a data series to the frequency domain and is very closely related to the complex Morlet wavelet transform.

##### Formula:
δfk = (21 / n)k x δfmin
###### Where,

δfk - Frequency of k-th filter n - Number of filters per octave δfmin - Centre frequency of the first bin

##### Example:

Consider that the total number filters per octave is 3, frequency of filter as 4 and the center frequency of first bin as 4 Hz. Learn how to calculate the frequency of kth filter using constant Q spectral transform for the given values?

##### Given,

Number of Filters (n) = 3 Frequency of filter (k) = 4 Center Frequency of first bin (δfmin) = 4 Hz

##### To find,

Constant Q transform frequency of k-th filter

##### Solution:

Substitute the given values in the constant Q spectral transform formula, δfk = (21 / n)k x δfmin δfk = (21 / 3)4 * 4 δfk = (1.2599210499)4 * 4 δfk = 2.5198420998 * 4 δfk = 10.0793683991 Hz. Hence, the constant Q spectral transform value of kth filter is 10.0793683991 Hz.