In this paper, we cover the basics of signal path design in radio DSP. We begin by defining several fundamental parameters, including fractional RMS value, fractional gain and headroom. A quick introduction to headroom estimation, one of the more difficult tasks in signal path design, is also given. We then proceed with a detailed study of signal path design for three common DSP structures: a gain stage, an FIR filter and an IIR filter. A closed-form expression for the fractional gain (the principal means of headroom control) is given in each case. Finally, we derive the noise figures of the same three structures and also investigate how the noise figure of an IIR filter is affected by the choice of filter realization (direct form 1 vs. direct form 2). The results presented in the paper clearly demonstrate one of the major advantages of radio signal processing in the digital domain: the ability to control linearity (headroom) independently of noise figure.