diff --git a/doc/filters.texi b/doc/filters.texi
index 30982cb6ab..ba31ed1316 100644
--- a/doc/filters.texi
+++ b/doc/filters.texi
@@ -585,6 +585,12 @@ adelay=0|500S|700S
 @end example
 @end itemize
 
+@section aderivative, aintegral
+
+Compute derivative/integral of audio stream.
+
+Applying both filters one after another produces original audio.
+
 @section aecho
 
 Apply echoing to the input audio.
diff --git a/libavfilter/Makefile b/libavfilter/Makefile
index b2d6756e79..717aa83359 100644
--- a/libavfilter/Makefile
+++ b/libavfilter/Makefile
@@ -35,6 +35,8 @@ OBJS-$(CONFIG_ACOPY_FILTER)                  += af_acopy.o
 OBJS-$(CONFIG_ACROSSFADE_FILTER)             += af_afade.o
 OBJS-$(CONFIG_ACRUSHER_FILTER)               += af_acrusher.o
 OBJS-$(CONFIG_ADELAY_FILTER)                 += af_adelay.o
+OBJS-$(CONFIG_ADERIVATIVE_FILTER)            += af_aderivative.o
+OBJS-$(CONFIG_AINTEGRAL_FILTER)              += af_aderivative.o
 OBJS-$(CONFIG_AECHO_FILTER)                  += af_aecho.o
 OBJS-$(CONFIG_AEMPHASIS_FILTER)              += af_aemphasis.o
 OBJS-$(CONFIG_AEVAL_FILTER)                  += aeval.o
diff --git a/libavfilter/af_aderivative.c b/libavfilter/af_aderivative.c
new file mode 100644
index 0000000000..a591515cbf
--- /dev/null
+++ b/libavfilter/af_aderivative.c
@@ -0,0 +1,207 @@
+/*
+ * This file is part of FFmpeg.
+ *
+ * FFmpeg is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * FFmpeg is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with FFmpeg; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
+ */
+
+#include "audio.h"
+#include "avfilter.h"
+#include "internal.h"
+
+typedef struct ADerivativeContext {
+    const AVClass *class;
+    AVFrame *prev;
+    void (*filter)(void **dst, void **prv, const void **src,
+                   int nb_samples, int channels);
+} ADerivativeContext;
+
+static int query_formats(AVFilterContext *ctx)
+{
+    AVFilterFormats *formats = NULL;
+    AVFilterChannelLayouts *layouts = NULL;
+    static const enum AVSampleFormat derivative_sample_fmts[] = {
+        AV_SAMPLE_FMT_S16P, AV_SAMPLE_FMT_FLTP,
+        AV_SAMPLE_FMT_S32P, AV_SAMPLE_FMT_DBLP,
+        AV_SAMPLE_FMT_NONE
+    };
+    static const enum AVSampleFormat integral_sample_fmts[] = {
+        AV_SAMPLE_FMT_FLTP, AV_SAMPLE_FMT_DBLP,
+        AV_SAMPLE_FMT_NONE
+    };
+    int ret;
+
+    formats = ff_make_format_list(strcmp(ctx->filter->name, "aintegral") ?
+                                  derivative_sample_fmts : integral_sample_fmts);
+    if (!formats)
+        return AVERROR(ENOMEM);
+    ret = ff_set_common_formats(ctx, formats);
+    if (ret < 0)
+        return ret;
+
+    layouts = ff_all_channel_counts();
+    if (!layouts)
+        return AVERROR(ENOMEM);
+
+    ret = ff_set_common_channel_layouts(ctx, layouts);
+    if (ret < 0)
+        return ret;
+
+    formats = ff_all_samplerates();
+    return ff_set_common_samplerates(ctx, formats);
+}
+
+#define DERIVATIVE(name, type)                                          \
+static void aderivative_## name ##p(void **d, void **p, const void **s, \
+                                    int nb_samples, int channels)       \
+{                                                                       \
+    int n, c;                                                           \
+                                                                        \
+    for (c = 0; c < channels; c++) {                                    \
+        const type *src = s[c];                                         \
+        type *dst = d[c];                                               \
+        type *prv = p[c];                                               \
+                                                                        \
+        for (n = 0; n < nb_samples; n++) {                              \
+            const type current = src[n];                                \
+                                                                        \
+            dst[n] = current - prv[0];                                  \
+            prv[0] = current;                                           \
+        }                                                               \
+    }                                                                   \
+}
+
+DERIVATIVE(flt, float)
+DERIVATIVE(dbl, double)
+DERIVATIVE(s16, int16_t)
+DERIVATIVE(s32, int32_t)
+
+#define INTEGRAL(name, type)                                          \
+static void aintegral_## name ##p(void **d, void **p, const void **s, \
+                                  int nb_samples, int channels)       \
+{                                                                     \
+    int n, c;                                                         \
+                                                                      \
+    for (c = 0; c < channels; c++) {                                  \
+        const type *src = s[c];                                       \
+        type *dst = d[c];                                             \
+        type *prv = p[c];                                             \
+                                                                      \
+        for (n = 0; n < nb_samples; n++) {                            \
+            const type current = src[n];                              \
+                                                                      \
+            dst[n] = current + prv[0];                                \
+            prv[0] = dst[n];                                          \
+        }                                                             \
+    }                                                                 \
+}
+
+INTEGRAL(flt, float)
+INTEGRAL(dbl, double)
+
+static int config_input(AVFilterLink *inlink)
+{
+    AVFilterContext *ctx = inlink->dst;
+    ADerivativeContext *s = ctx->priv;
+
+    switch (inlink->format) {
+    case AV_SAMPLE_FMT_FLTP: s->filter = aderivative_fltp; break;
+    case AV_SAMPLE_FMT_DBLP: s->filter = aderivative_dblp; break;
+    case AV_SAMPLE_FMT_S32P: s->filter = aderivative_s32p; break;
+    case AV_SAMPLE_FMT_S16P: s->filter = aderivative_s16p; break;
+    }
+
+    if (strcmp(ctx->filter->name, "aintegral"))
+        return 0;
+
+    switch (inlink->format) {
+    case AV_SAMPLE_FMT_FLTP: s->filter = aintegral_fltp; break;
+    case AV_SAMPLE_FMT_DBLP: s->filter = aintegral_dblp; break;
+    }
+
+    return 0;
+}
+
+static int filter_frame(AVFilterLink *inlink, AVFrame *in)
+{
+    AVFilterContext *ctx = inlink->dst;
+    ADerivativeContext *s = ctx->priv;
+    AVFilterLink *outlink = ctx->outputs[0];
+    AVFrame *out = ff_get_audio_buffer(outlink, in->nb_samples);
+
+    if (!out) {
+        av_frame_free(&in);
+        return AVERROR(ENOMEM);
+    }
+    av_frame_copy_props(out, in);
+
+    if (!s->prev) {
+        s->prev = ff_get_audio_buffer(inlink, 1);
+        if (!s->prev) {
+            av_frame_free(&in);
+            return AVERROR(ENOMEM);
+        }
+    }
+
+    s->filter((void **)out->extended_data, (void **)s->prev->extended_data, (const void **)in->extended_data,
+              in->nb_samples, in->channels);
+
+    av_frame_free(&in);
+    return ff_filter_frame(outlink, out);
+}
+
+static av_cold void uninit(AVFilterContext *ctx)
+{
+    ADerivativeContext *s = ctx->priv;
+
+    av_frame_free(&s->prev);
+}
+
+static const AVFilterPad aderivative_inputs[] = {
+    {
+        .name         = "default",
+        .type         = AVMEDIA_TYPE_AUDIO,
+        .filter_frame = filter_frame,
+        .config_props = config_input,
+    },
+    { NULL }
+};
+
+static const AVFilterPad aderivative_outputs[] = {
+    {
+        .name = "default",
+        .type = AVMEDIA_TYPE_AUDIO,
+    },
+    { NULL }
+};
+
+AVFilter ff_af_aderivative = {
+    .name          = "aderivative",
+    .description   = NULL_IF_CONFIG_SMALL("Compute derivative of input audio."),
+    .query_formats = query_formats,
+    .priv_size     = sizeof(ADerivativeContext),
+    .uninit        = uninit,
+    .inputs        = aderivative_inputs,
+    .outputs       = aderivative_outputs,
+};
+
+AVFilter ff_af_aintegral = {
+    .name          = "aintegral",
+    .description   = NULL_IF_CONFIG_SMALL("Compute integral of input audio."),
+    .query_formats = query_formats,
+    .priv_size     = sizeof(ADerivativeContext),
+    .uninit        = uninit,
+    .inputs        = aderivative_inputs,
+    .outputs       = aderivative_outputs,
+};
diff --git a/libavfilter/allfilters.c b/libavfilter/allfilters.c
index f28f6e47ee..5d3ed0a8a2 100644
--- a/libavfilter/allfilters.c
+++ b/libavfilter/allfilters.c
@@ -30,6 +30,7 @@ extern AVFilter ff_af_acopy;
 extern AVFilter ff_af_acrossfade;
 extern AVFilter ff_af_acrusher;
 extern AVFilter ff_af_adelay;
+extern AVFilter ff_af_aderivative;
 extern AVFilter ff_af_aecho;
 extern AVFilter ff_af_aemphasis;
 extern AVFilter ff_af_aeval;
@@ -39,6 +40,7 @@ extern AVFilter ff_af_afir;
 extern AVFilter ff_af_aformat;
 extern AVFilter ff_af_agate;
 extern AVFilter ff_af_aiir;
+extern AVFilter ff_af_aintegral;
 extern AVFilter ff_af_ainterleave;
 extern AVFilter ff_af_alimiter;
 extern AVFilter ff_af_allpass;
