Question

when a square wave signal is given to a low pass filter what is its output

Answer 1

It depends on the Band Width, BW, of the low pass filter. The major components of a square wave is it's Fundamental to the Fifth harmonic, therefore if the BW of the low pass filter is equal the Fifth harmonic then the output would be essentially a square wave. If one is to use the Nyquist criteria the BW would have to be ten times the fundaments, or two times the fifth harmonic.

Answer 2

Ken's answer is correct.

But in the case when the bandwidth of the filter (usually called the "corner frequency" or "cutoff frequency") is less than the Nyquist frequency Ken mentioned, the output will look more and more like a sine wave. If the BW is at or below the fundamental frequency of the square wave, the output will be a sine wave of the fundamental frequency. There may, however, be harmonic distortion in that output waveform. The amount of harmonic distortion will be a function of how sharply the filter rolls off above its cutoff frequency. The sharper the rolloff, the less harmonic distortion exhibited by the output waveform. Unless the cutoff frequency is higher than the fundamental frequency and the filter is of a very high order (very steep rolloff), the output waveform magnitude will be less than that of the input waveform.