We demonstrate an optical mixing system for measuring properties of sparse radio frequency (RF) signals using compressive sensing (CS). Two types of sparse RF signals are investigated: (1) a signal that consists of a few 0.4 ns pulses in a 26.8 ns window and (2) a signal that consists of a few sinusoids at different frequencies. The RF is modulated onto the intensity of a repetitively pulsed, wavelength-chirped optical field, and time-wavelength-space mapping is used to map the optical field onto a 118-pixel, one-dimensional spatial light modulator (SLM). The SLM pixels are programmed with a pseudo-random bit sequence (PRBS) to form one row of the CS measurement matrix, and the optical throughput is integrated with a photodiode to obtain one value of the CS measurement vector. Then the PRBS is changed to form the second row of the mixing matrix and a second value of the measurement vector is obtained. This process is performed 118 times so that we can vary the dimensions of the CS measurement matrix from $1\times 118$ to $118\times 118$ (square). We use the penalized ${\ell }_1$ norm method with stopping parameter $\lambda$ (also called basis pursuit denoising) to recover pulsed or sinusoidal RF signals as a function of the small dimension of the measurement matrix and stopping parameter. For a square matrix, we also find that penalized ${\ell }_1$ norm recovery performs better than conventional recovery using matrix inversion.