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1.4. Normalized Frequency

The notation in Equation 1.4 is based on the concept of dividing the unit circle into N equal arc segments. We can derive an equivalent expression simply by observing that the digital frequency


can be normalized by dividing both sides of the equation by the sample frequency fS to arrive at

Both sides of Equation 1.7 are now expressed as a fraction between 0 and 0.5. We can drop the subscript K such that fK becomes f. When we do we can think of both f and fS as being two analog frequencies whose ratio just happens to be k/N. This notation is useful if the unit circle is not specifically considered in the derivation of digital frequencies. The two methods of notation are equivalent, as illustrated in Equation 1.8.

It’s a matter of preference. Either notation is correct. This book uses both notations where appropriate.

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