Explanation:

The statement is true. The oscillatory behavior near the band edge of the low pass filter is indeed known as the Gibbs phenomenon.

The Gibbs Phenomenon:
The Gibbs phenomenon is a characteristic behavior that occurs in the Fourier series representation of a signal or function. It is characterized by oscillations or overshoots near discontinuities or sharp edges in the signal.

Low Pass Filter:
A low pass filter is a type of electronic filter that allows low-frequency signals to pass through while attenuating higher-frequency signals. It is commonly used in signal processing and communication systems to remove high-frequency noise or to limit the bandwidth of a signal.

Oscillatory Behavior near the Band Edge:
When a low pass filter is designed with a specific cutoff frequency, it starts to attenuate frequencies above that cutoff frequency. Near the band edge, where the filter starts to attenuate the higher frequencies, an oscillatory behavior can be observed.

Explanation:
At the band edge, the low pass filter exhibits a transition region where the frequency response changes from passband to stopband. This transition region is characterized by oscillations or ripples in the frequency response.

These oscillations or ripples are a result of the Gibbs phenomenon. When a filter is designed with a sharp transition between the passband and stopband, it introduces discontinuities or sharp edges in the frequency response. The Fourier series representation of these discontinuities leads to oscillatory behavior near the band edge.

The Gibbs phenomenon is a fundamental property of Fourier series representation and is not limited to low pass filters. It occurs whenever there are sharp transitions or discontinuities in the signal or function being represented.

In summary, the oscillatory behavior near the band edge of a low pass filter is indeed known as the Gibbs phenomenon. It is a result of the sharp transition between the passband and stopband, leading to oscillations or ripples in the frequency response.