We propose a novel cepstral representation called the uniform discrete cepstrum (UDC) to represent the timbre of sound sources in a sound mixture. Different from ordinary cepstrum and MFCC which have to be calculated from the full magnitude spectrum of a source after source separation, UDC can be calculated directly from isolated spectral points that are likely to belong to the source in the mixture spectrum (e.g., non-overlapping harmonics of a harmonic source). Existing cepstral representations that have this property are discrete cepstrum and regularized discrete cepstrum, however, compared to the proposed UDC, they are not as effective and are more complex to compute. The key advantage of UDC is that it uses a more natural and locally adaptive regularizer to prevent it from overfitting the isolated spectral points. We derive the mathematical relations between these cepstral representations, and compare their timbre modeling performances in the task of instrument recognition in polyphonic audio mixtures. We show that UDC and its mel-scale variant MUDC significantly outperform all the other representations.