The anti-symmetric condition with M even is not used in the design of the low pass linear-phase FIR filter.

Explanation:
- The anti-symmetric condition refers to the symmetry property of a filter's impulse response. An anti-symmetric filter has a symmetric impulse response, meaning that the values of the impulse response alternate in sign around its midpoint.
- The linear-phase property of a filter means that all frequencies of the input signal are delayed by the same amount, resulting in the output signal having a constant phase shift across all frequencies.
- An FIR (Finite Impulse Response) filter is a type of digital filter where the impulse response has finite duration.
- In the design of linear-phase FIR filters, the impulse response is often made symmetric to achieve linear phase characteristics.
- However, in the case of a low pass filter, the anti-symmetric condition with M even is not used. Here's why:

Low pass filter:
- A low pass filter allows low-frequency components of a signal to pass through while attenuating higher-frequency components.
- In the design of a low pass filter, it is desirable to have a symmetric impulse response to achieve linear phase characteristics.
- The symmetric impulse response helps in achieving a flat passband and a sharp transition from the passband to the stopband.
- By using a symmetric impulse response, the linear-phase property can be preserved, ensuring that all frequencies of the input signal are delayed by the same amount.
- The anti-symmetric condition with M even is not used in the design of a low pass filter because it would introduce a phase distortion that is undesirable for a low pass filter.
- The anti-symmetric condition would result in a non-linear phase response, where different frequencies of the input signal would experience different amounts of delay, leading to distortions in the output signal.

Conclusion:
The anti-symmetric condition with M even is not used in the design of a low pass linear-phase FIR filter because it would introduce phase distortions.