An apparatus for estimating an impulse response of a linear system, wherein the apparatus comprises a measurement block configured to generate a transmit signal on the basis of a first sequence and to send the transmit signal onto the linear system, wherein the measurement block is configured to obtain a receive signal as a feedback from the linear system and to multiply the receive signal with a second sequence, to obtain a modified receive signal, wherein the second sequence is different from the first sequence, wherein the measurement block is configured to analog-to-digital convert, ADC, an integration result in order to obtain a sample value, the integration result being based on an integration of the modified receive signal over a period (T s) of time, and wherein the apparatus is configured to obtain an estimate of the impulse response on the basis of a plurality of sample values, wherein the first sequence and the second sequence are synchronized with each other and/or are generated from a common system clock signal (20, f c) and/or are synchronized with a common system clock signal (20, f c), wherein the measurement block is configured to perform a clock division by dividing the common system clock signal by a first divider factor parameter (17, S) to obtain a sampling clock signal (21, f s) to control the ADC conversion and/or to define the period (T s) of time of the integration of the modified receive signal, wherein the first sequence is associated to a first linear signal model (D, 13), and the second sequence is associated to a second linear model (φ, 14), so as to obtain the estimate of the impulse response on the basis of a relationship between the plurality (29, b) of sample values, the first linear signal model (D, 13), and the second linear model (φ, 14), wherein the first linear model (D, 13) is described by a first sparse representation operator and the second linear model (φ, 14) is described by a second sparse representation operator, wherein the first sparse representation operator is obtained through a factorization which involves at least one Hadamard matrix or Hadamard transform. wherein the apparatus comprises a measurement block configured to generate a transmit signal on the basis of a first sequence and to send the transmit signal onto the linear system, wherein the measurement block is configured to obtain a receive signal as a feedback from the linear system and to multiply the receive signal with a second sequence, to obtain a modified receive signal, wherein the second sequence is different from the first sequence, wherein the measurement block is configured to analog-to-digital convert, ADC, an integration result in order to obtain a sample value, the integration result being based on an integration of the modified receive signal over a period (T s) of time, and wherein the apparatus is configured to obtain an estimate of the impulse response on the basis of a plurality of sample values, wherein the first sequence and the second sequence are synchronized with each other and/or are generated from a common system clock signal (20, f c) and/or are synchronized with a common system clock signal (20, f c), wherein the measurement block is configured to perform a clock division by dividing the common system clock signal by a first divider factor parameter (17, S) to obtain a sampling clock signal (21, f s) to control the ADC conversion and/or to define the period (T s) of time of the integration of the modified receive signal, wherein the first sequence is associated to a first linear signal model (D, 13), and the second sequence is associated to a second linear model (φ, 14), so as to obtain the estimate of the impulse response on the basis of a relationship between the plurality (29, b) of sample values, the first linear signal model (D, 13), and the second linear model (φ, 14), wherein the first linear model (D, 13) is described by a first sparse representation operator and the second linear model (φ, 14) is described by a second sparse representation operator, wherein the first sparse representation operator is obtained through a factorization which involves at least one Hadamard matrix or Hadamard transform.