A novel chirped-pulse Fourier transform microwave (CP-FTMW) spectrometer has been constructed to cover the Ka-band (26.5 GHz–40 GHz) for use in the CRESUCHIRP project, which aims to study the branching ratios of reactions at low temperatures using the chirped-pulse in uniform flow technique. The design takes advantage of recent developments in radio-frequency components, notably, high-frequency, high-power solid-state amplifiers. The spectrometer had a flatness of 5.5 dB across the spectral range, produced harmonic signals below −20 dBc, and the recorded signal scaled well to 6 × 106 averages. The new spectrometer was used to determine pressure broadening coefficients with a helium collider at room temperature for three molecules relevant to astrochemistry, applying the Voigt function to fit the magnitude of the Fourier-transformed data in the frequency domain. The pressure broadening coefficient for carbonyl sulfide was determined to be (2.45 ± 0.02) MHz mbar-1 at room temperature, which agreed well with previous measurements. Pressure broadening coefficients were also determined for multiple transitions of vinyl cyanide and benzonitrile. Additionally, the spectrometer was coupled with a cold, uniform flow from a Laval nozzle. The spectrum of vinyl cyanide was recorded in the flow, and its rotational temperature was determined to be (24 ± 11) K. This temperature agreed with a prediction of the composite temperature of the system through simulations of the experimental environment coupled with calculations of the solution to the optical Bloch equations. These results pave the way for future quantitative studies in low-temperature and high-pressure environments using CP-FTMW spectroscopy.