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This paper designs and experimentally demonstrates an electronic hardware architecture to measure impulse signals without resorting to high-speed analog-to-digital converters (ADCs). The proposed architecture is based on a frequency-domain approach. It consists of multiple channels to down-convert the input signal, each of which obtains a small portion of the input's spectrum. Overlapping bands are designated in between every two adjacent channels, so that multiple narrow-band outcomes can be accurately merged to construct the entire spectrum through postprocessing. The resultant complex-valued spectrum is equivalent to that where the impulses are directly measured in the time domain. The architecture in this paper resembles traditional superheterodyne receivers, and hence, its circuit implementation is simple and robust and has low cost. In our circuit implementation, all the components involved (like oscillators and mixers) are commercially available and have low costs. The circuit is tested by two types of input impulses, both having spectra centered at 2.1 GHz. The input signals' spectra (including both magnitude and phase) obtained by our circuit show excellent agreement with the data measured by a 40-GHz oscilloscope. When the input signal-to-noise ratio is as low as 2 dB, the output of our frequency-domain approach is equivalent to that of a 4-b high-speed ADC.