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Signal processing tools working directly on encrypted data could provide an efficient solution to application scenarios where sensitive signals must be protected from an untrusted processing device. In this paper, we consider the data expansion required to pass from the plaintext to the encrypted representation of signals, due to the use of cryptosystems operating on very large algebraic structures. A general composite signal representation allowing us to pack together a number of signal samples and process them as a unique sample is proposed. The proposed representation permits us to speed up linear operations on encrypted signals via parallel processing and to reduce the size of the encrypted signal. A case study-1-D linear filtering-shows the merits of the proposed representation and provides some insights regarding the signal processing algorithms more suited to work on the composite representation.