The Aliasing Illustration using a signal spectrum band-limited to 4 kHz and the sampling rate of 8 kHz. The signal is completely band-limited to 4 kHz so that there is no overlapping in spectrum of the sampled signal.
The signal has an authentic, desirable, 1 kHz component. As it is not perfectly band-limited to 4 kHz it has another genuine but undesirable 7 kHz component. Because of the first pair of replicas (centered at 8 kHz and -8 kHz) this 7kHz component seems as if it were a 1kHz component - or we can say that the 7 kHz component is an alias of 1kHz. Therefore the first alias of the 1 kHz frequency can be given by 8 kHz - 1 kHz = 7 kHz.
Because of the second pair of replicas at 16 kHz and -16 kHz the 15k component in original signal appears as if it were a 1k component - it is another alias of 1k. This 2nd alias of the 1 kHz frequency can be given by 16 kHz - 1 kHz = 15 kHz. The next alias is (3 x8 - 1) kHz = 23 kHz.
Generally for any frequency F1 within the base band (in this case the frequency from 0 to 4000 Hz) its aliases can be given by
Alias = kFs - F1, k is an integer > 0
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