An encoder for encoding a parametric spectral representation (f) of auto-regressive coefficients that partially represent an audio signal. The encoder includes a low-frequency encoder configured to quantize elements of a part of the parametric spectral representation that correspond to a low-frequency part of the audio signal. It also includes a high-frequency encoder configured to encode a high-frequency part (fH) of the parametric spectral representation (f) by weighted averaging based on the quantized elements ({circumflex over (f)}L) flipped around a quantized mirroring frequency ({circumflex over (f)}m), which separates the low-frequency part from the high-frequency part, and a frequency grid determined from a frequency grid codebook in a closed-loop search procedure. Described are also a corresponding decoder, corresponding encoding/decoding methods and UEs including such an encoder/decoder.