The power of a signal is determined by its amplitude and frequency content. In the case of a square wave with many harmonics versus white noise, it is important to consider how power is defined for each type of signal.
A square wave with many harmonics consists of a fundamental frequency and its odd harmonics (e.g., 3rd, 5th, 7th, etc.), with decreasing amplitudes as the harmonic number increases. The power of a periodic signal like a square wave is typically measured as the average power over a period. Since the harmonic amplitudes decrease with increasing frequency, the power of a square wave with many harmonics tends to concentrate more in the lower-frequency components, particularly around the fundamental frequency.
On the other hand, white noise is a random signal that contains equal power across all frequencies within its bandwidth. White noise has a constant power spectral density, meaning it has equal power at all frequencies. The power of white noise is typically measured as the average power over a specified bandwidth.
Comparing the power of a square wave with many harmonics to white noise can be challenging, as they have different frequency characteristics. The square wave will have more power concentrated in the lower-frequency components, while white noise has equal power across all frequencies.
In general, if the bandwidth of the white noise is sufficiently large, it can contain a significant amount of power across a wide range of frequencies. However, if the square wave has a large number of harmonics and its fundamental frequency is within the bandwidth of the white noise, the square wave can have more power within that specific frequency range.
It's important to note that power is just one aspect of comparing signals, and other factors such as perception, signal-to-noise ratio, and specific applications may play a significant role in determining which signal is more significant or relevant in a given context.