Using the convolution property, find the spectrum for
$$w(t)= \sin(2\pi f_1 t) \cos(2\pi f_2 t).$$
I'm confused on how to solve this question. Can you give me any aproach?
2026-04-07 08:01:27.1775548887
Finding spectrum using the convolution property
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The Fourier Transform of the product of two signals (functions) is the convolution of their spectra, i.e. the convolution of their individual Fourier Transforms. The spectra of $sin(2\pi f_1t), cos(2 \pi f_2t)$ are well known (dirac functions at appropriate locations and with appropriate coefficients) and convolving them is also easy, using the property of the delta function $\delta(t-t_0) * f(t)=f(t_0)$ where $*$ denotes convolution.