In this paper, we analyze a mixer-first receiver, which includes passive polyphase mixers, low-noise baseband amplifiers, and baseband circulant-symmetric polyphase feedback. This analysis is performed for input frequencies located around any harmonic frequency of the local oscillator. From this, circuits and methods are introduced, which allow control of the receiver's harmonic input impedance through the use of resistive-capacitive (RC) baseband feedback networks. We show that the harmonic input admittance of the mixer-first receiver is related to the discrete Fourier transform of the baseband circulant. This Fourier relationship allows control of the harmonic impedance response across frequencies. The noise figure of the receiver with circulant-symmetric feedback can approach that of an equivalent mixer-first receiver having harmonic feedforward cancellation without the additional power consumption of a cancellation stage. Harmonic impedance shaping can improve the blocker tolerance by decreasing the harmonic conversion gain. A single design can be reconfigured to use these techniques for fundamental-frequency or subharmonic operation. Derivations for impedance, conversion gain, and noise figure are included and a linear time-invariant circuit model is introduced. These are validated through circuit simulation using a combination of 45-nm silicon-on-insulator CMOS technology and behavioral baseband models.