Spatial Frequency and the Fourier Idea

How fast does an image vary

Any function is a sum of sines

Fourier's own ramp

Waves in one and two dimensions

In the Fourier series $t/2 = \sin t - \frac{1}{2}\sin 2t + \frac{1}{3}\sin 3t - \dots$, what happens to the curve when you keep only the first term and drop the rest?

A grayscale image of size $64 \times 48$ pixels contains the wave $s_{u,v}[n,m] = \sin(2\pi(\frac{3n}{64} + \frac{0m}{48}))$. What does this wave look like?

The Fourier series of the ramp $t/2$ on $(0, \pi)$ is $\sin t - \frac{1}{2}\sin 2t + \frac{1}{3}\sin 3t - \dots$. Write the magnitude of the coefficient multiplying $\sin 2t$ as a decimal.